Wouldn't it be great if it was something that silly and simple

Did you find a solution here? Interested for my own education.

I am interested too as I am having an issue like this also.

I always ran my TG with both battery switches on 1. That isolates each battery to each engine. I would only switch to both to start when a battery was low from running the stereo for hours. I also had a ground between the two engines, but have seen others without. Good luck, electrical issues suck!

I went through a problem with having a battery go bad recently, at least it turned out to be a bad battery.

Try to start the port engine and all I get is a click (this is with each engine on it's own battery, as in both switches pointing to 1). I switch the port engine to battery 2 (which is the stbd battery - I double checked the wiring and this is correct). Still just a "click" of the starter solenoid. I start the stbd engine, which readily cranks over, and try again to start the port engine, still just a "click" or maybe a "stuttering click". I double checked all power and ground cables, all good. I am now convinced that the starter had suddenly gone bad. I just couldn't believe that was the suddenly the problem, so I swapped batteries and the problem swapped also, now the port would fire right up (Great, at least the starter isn't bad), but the stbd just clicked and it didn't matter what I did with the battery switches. I then came up with the idea to run a jumper cable from one engine to the other, as a ground to ground, and suddenly my problems were gone. Everything worked as it should. I still cannot believe that all of the battery grounds are not combined somewhere, but evidently they are not.

Long story short, I ran a ground cable from engine to engine and now my battery switches work as they should.

if you switch a battery selector to another engine or battery without having the blocks tied together you dont have a complete circuit, glad you got it fixed much easier than changing a starter

I used to run a negative cable between engines, with EFI it didn`t seem like a good idea so I disconnected it . (interference, backfeeding etc )
Haven`t noticed any ill affects

I can tell you I have a ground between motors. Still struggling with this as it is quirky. Been using boat every weekend and runs great. Just sometimes when one is running and trying to start other it will pull running motor down. Both motors are running on #1 selector switch. If I start both at same time, no issues and they will both immediately fire up. I will eventually figure it out :)

they only thing the perko switch does is switch +12 vdc from one terminal to another, so If you switch engine 1 to battery 2 where is the return, engine 1 has the negative of battery1, if the engines aren't tied together I dont see how it completes are circuit.

Negatives on all my batteries are connected together so it completes the circuit. My engines do not have separate ground cable connecting them.