Idle RPM sensitivity to signalling?

I have a 95 Grand Prix GTP, and if I'm signalling at idle (in gear, my
foot on the brakeat a dead stop) my RPM decreases by about 50 RPM when
the signal light is lit and cycles back up when it turns off and
continues during the periodicity of the signalling. My dash lights also
slightly dim with the same trend. My question is, is this normal?
Should the engine idle and interior accessory lights really be this
sensitive to such a small electrical draw? I have checked my battery at
idle and it's charging at 13.8V, and I haven't had any other electrical
problems. However, I do have some other erratic idling when not
signalling, so if this could all be attributed to the same electrical
problem I'd love to figure it out. Thanks.

407