Turn signals not working, blowing fuse

Just so I’m clear, you’re saying to remove the bulkhead connector and check each of those terminals for continuity?
You tell us.
What are you trying learn with these continuity measurements?

I'm still not sure what you measured when you got a full ohm on the meter.
However you posted that removing the bulkhead solved the short. OK, so why did you stop there?
Was this at the same time as disconnecting the radio? which I thought you had already disconnected.

It seems to me that you're not sure of the reason we probe for continuity to ground.
Likewise why we have suggested disconnecting things.

So you tell us.
Assuming removing the bulkead connector solved the problem, what might be learned by checking the terminals?
Also, if you know, tell us what else the reverse light switch does?