This post is not about running livescope on a starting battery, it is about running on a dedicated lithium battery.
And even then, a voltage sag when starting the motor is a weak or too small of a battery. You can have 0 gauge wiring to your fishfinder and it will still sag to whatever the battery goes to when your 30A starter is engaged... Having thinner wire to your fishfinder does not make your voltage drop when you start the engine.
On top of all of that, why do you care if your livescope transducer voltage is dropping when you start the outboard? I dont know if I have ever been watching sonar while starting the motor.
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