Voltage drop?

Your description sounds like the battery terminal clamp has a bad connection. You say you can wiggle it and the power returns? In that case what is moving when you wiggle the cable? The cable in the connector? The connector on the post or does the post move as well? The last one would be the worst as that would mean the battery needs to be replaced as the internal connection has failed and those cannot be repaired. The others mean that you need to clean and tighten the connectors or replace the connection if the cable is loose in it.

If the cable moves at all I would start looking it over closely, what generally happens with cables is that any acid leaks at the battery will wick into the strands and corrode the metal inside, from the outside it still looks good but inside it's just the mush left behind. Remove the heat shrink and tape and see if maybe someone tried to add on a section or if it's corroded under it.