While upgrading the wiring will certainly help. The OP's problem still sounds like a battery to me.
Here is the proper technique for testing a battery.
Lengthy, had to cut/paste out of a PDF file which I was unable to link.
Note: the only method to properly check a deep cycle battery is under load.
I've had fishing boats with trolling motor and electronics for decades. I've been using a digital Schumacher unit to test and help maintain the 3 batteries on my Hewes Redfisher for years. I haven't done a test on my Hawk's 2x Optima Blue tops to date.
DEEP CYCLE BATTERIES
3. HOW DO I TEST A BATTERY?
There are six simple steps in testing a deep cycle battery-inspect, recharge, remove surface charge, measure the state-of-charge, load test, and recharge. If you have a non-sealed battery, it is highly recommended that you use a good quality temperature compensated hydrometer; these can be purchased at an auto parts store for between $5 and $20. A hydrometer is a float type device used to determine the state-of-charge by measuring the specific gravity of the electrolyte in each cell. It is a very accurate way of determining a battery's state-of-charge and its weak or dead cells. To troubleshoot charging or electrical systems or if you have a sealed battery, you will need a digital voltmeter with 0.5% or better accuracy. A digital voltmeter can be purchased at an electronics store like Radio Shack for between $20 and $200. Analog voltmeters are not accurate enough to measure the millivolt differences of a battery's state-of-charge or the output of the charging system. The purchase of a battery load tester is optional; if you use a golf cart or electric trolling motor every day, buy one.
3.1. INSPECT
Visually inspect for obvious problems. For example, is there a loose or broken alternator belt, electrolyte levels BELOW the top of the plates, corroded or swollen cables, corroded terminal clamps, dirty or wet battery top, loose hold-down clamps, loose cable terminals, or leaking or damaged battery case? If the electrolyte levels are low in non-sealed batteries, allow the battery to cool and add DISTILLED water to the level indicated by the battery manufacturer. If this is not indicated, use 1/4 inch (7 mm) BELOW the bottom of the plastic filler tube (vent wells). The plates need to be covered at all times. Avoid OVERFILLING, especially in hot climates, because heat will cause the electrolyte to expand and overflow.
3.2. RECHARGE
Recharge the battery to 100% state-of-charge. If the battery has a difference of .03 specific gravity reading between the lowest and highest cell, then you should equalize it. (Please see Section 6.)
3.3. REMOVE SURFACE CHARGE
Surface charge is the uneven mixture of sulfuric acid and water within the surface of the plates as a result of charging or discharging. It will make a weak battery appear good or a good battery appear bad. You need to eliminate the surface charge by one of the following methods:
3.3.1. Allow the battery to sit for four to twelve hours to allow for the surface charge to dissipate.
3.3.2. Apply a load that is 33% of the ampere-hour capacity for five minutes and wait five to ten minutes.
3.3.3. With a battery load tester, apply a load of at least one half the battery's CCA rating for 15 seconds and wait five to ten minutes.
3.4. MEASURE THE STATE-OF-CHARGE
If the battery's electrolyte is above 110o F (43.3o C), allow it to cool. To determine the battery's state-of-charge with the battery's electrolyte temperature at 80o F (26.7o C), use the following table. The table assumes that a 1.265 specific gravity reading is a fully charged, wet, lead-acid battery. For other electrolyte temperatures, use the Temperature Compensation table below to adjust the Open Circuit Voltage or Specific Gravity readings. The Open Circuit Voltage will vary for gel cell and AGM type batteries so check the manufacturer's specifications.
Digital Voltmeter Open Circuit Voltage Approximate State-of-Charge Hydrometer Average Cell Specific Gravity Electrolyte Freeze Point 12.65 100% 1.265 -75o F (-59.4o C) 12.45 75% 1.225 -55o F (-48.3o C) 12.24 50% 1.190 -34o F (-36.7o C) 12.06 25% 1.155 -16o F (-26.7o C) 11.89 Discharged 1.120 -10o F (-23.3o C) STATE-OF-CHARGE [Source: BCI]
Electrolyte Temperature Fahrenheit Electrolyte Temperature Celsius Add or Subtract to Hydrometer's SG Reading Add or Subtract to Digital Voltmeter's Reading 160o 71.1o +.032 +.192 150o 65.6o +.028 +.168 140o 60.0o +.024 +.144 130o 54.4o +.020 +.120 120o 48.9o +.016 +.096 110o 43.3o +.012 +.072 100o 37.8o +.008 +.048 90o 32.2o +.004 +.024 80o 26.7o 0 0 70o 21.1o -.004 -.024 60o 15.6o -.008 -.048 50o 10o -.012 -.072 40o 4.4o -.016 -.096 30o -1.1o -.020 -.120 20o -6.7o -.024 -.144 10o -12.2o -.028 -.168 0o -17.8o -.032 -.192
TEMPERATURE COMPENSATION
Electrolyte temperature compensation will vary depending on the battery manufacturer's recommendations. If you are using a NON-temperature compensated HYDROMETER, make the adjustments indicated in the table above. For example, at 30 o F (-1.1o C), the specific gravity reading would be 1.245 for a 100% state-of-charge. At 100 o F (37.8 o C), the specific gravity would be 1.273 for 100% state-of-charge. This is why using a temperature compensated hydrometer is highly recommended and more accurate. If you are using a DIGITAL VOLTMETER, make the adjustments indicated in the table above. For example, at 30 o F (-1.1o C), the voltage reading would be 12.53 for a 100% state-of-charge. At 100 o F (37.8 o C), the voltage would be 12.698 for 100% state-of-charge.
For non-sealed batteries, check the specific gravity in each cell with a hydrometer and average the readings. For sealed batteries, measure the Open Circuit Voltage across the battery terminals with an accurate digital voltmeter. This is the only way you can determine the state-of-charge. Some batteries have a built-in hydrometer, which only measures the state-of-charge in ONE of its six cells. If the built-in indicator is clear or light yellow, then the battery has a low electrolyte level and should be refilled and recharged before proceeding. If sealed, the battery should be replaced.
If the state-of-charge is BELOW 75%, using either the specific gravity or voltage test, or the built-in hydrometer indicates "bad" (usually dark), then the battery needs to be recharged BEFORE proceeding. You should also replace the battery if one or more of the following conditions occur:
3.4.1. If there is a .05 (sometimes expressed as 50 "points") or more difference in the specific gravity reading between the highest and lowest cell, you have a weak or dead cell(s). If you are really lucky, applying an EQUALIZING charge may correct this condition. (Please see Section 6.)
3.4.2. If the battery will not recharge to a 75% or more state-of-charge level or if the built-in hydrometer still does not indicate "good" (usually green, which is 65% state-of-charge or better).
If you know that a battery has spilled or "bubbled over" and the electrolyte has been replaced with water, you can replace the old electrolyte with new electrolyte and go back to Step 3.2 above. Battery electrolyte is a mixture of 25% sulfuric acid and distilled water. It is cheaper to replace the electrolyte than to buy a new battery.
3.4.3. If digital voltmeter indicates 0 volts, you have an open cell.
3.4.4. If the digital voltmeter indicates 10.45 to 10.65 volts, you probably have a shorted cell or a severely discharged battery. A shorted cell is caused by plates touching, sediment ("mud") build-up or "treeing" between the plates.
3.5. LOAD TEST
If the battery is fully charged or has a "good" built-in hydrometer indication, then you can test the capacity of the battery by applying a known load and measuring the time it take to discharge the battery until 20% capacity is remaining. Normally a discharge rate that will discharge a battery in 20 hours can be used. For example, if you have an 80-ampere-hour rated battery, then a load of four amps would discharge the battery in approximately 20 hours (or 16 hours down to the 20% level). New batteries can take up to 50 charge/discharge cycles before they reach their rated capacity. Depending on your application, batteries with 80% or less of their original capacity are considered to be bad.
3.6. RECHARGE
If the battery passes the load test, you should recharge it as soon as possible to restore it to peak performance and to prevent lead sulfation.