Battery and grounds....
In my opinion, this is one of the dumbest ways to set these twin engine boats up. If you look over your battery and starting system, you'll notice the battery sitting beside the starboard (right) motor. The positive and ground lead off to this starter system normally. But, where your batteries wiring connects to your port (left) engine, the ground strap actually bridges off your starboard engine, usually at the front around the magneto housing.
What I would recommend you do in the future. Measure the distance between the grounding lug on the back side of the starter of that port engine to your battery. Then, go to an automotive store and buy a grounding wire with the proper lugs and run directly from your battery to your port engine for a solid ground. Of course, you'll want some tie wraps to arrange your new wire in a nice way. Also, use a larger gage grounding wire than the one you have.
This also is a problem if you have a weaker battery. The voltage drop between the battery and the engine sitting the closest has less wire to the engine. Therefore, has less drop in voltage due to resistance. So, by design, it should always be the easiest engine to start. If the battery is really strong, you really should not be able to tell much difference.
Two ways of starting. I usually tell members to start that port engine first, unless you hear the starter dragging, trying to start (this could be due to a low charge). If that's the case, start the starboard engine first. Let it run for a few minutes, then try to start the port. The only thing I have noticed about the twin engine is motor noise. Once you have one engine running, it's pretty hard to hear if you are having a starting issue or any strange sounds off the none running engine.
So, if you think you have a battery issue, take it down and load test it for free at your local Advanced Auto parts. If the battery is good, replace the way your port motor is grounded..............:cheers: