I've noticed that even at speed using my blinker will cause the voltmeter in the gauge cluster to dip pretty significantly and actually causes a change in the tone of the fuel pump. My experience with other old cars would tell me that this is likely a grounding issue, but I'm open to input if anyone has other suggestions.

I've found some information on RX-7 grounding, but primarily around FCs and FDs, eg: https://www.aaroncake.net/RX-7/grounding.htm. Does anyone have an FB-specific guide that might help me out?

 

Welcome to the board.

I would have said check your grounds first as well. Aaron Cake's writeup is a great place to start. It matters not that it's geared toward the FC, the concepts are universal. Get your hands on a shop manual for the Gen I cars (the FSM can be downloaded from Foxed.ca and/or you can get a Haynes manual) and give it a try.