64 Valiant charging and lighting/gauge issues

I'm going to guess "constant power to stereo" is memory of aftermarket head unit.
The horn power goes to the horn relay first. Another horn wire ( typically black ) is hot coming back inside to the horn switch. That switch grounds the wire which closes the relay and the horn blows. A ground path on this wire inside is supposed to close the relay and blow the horn. So if this is the wire that is tapped,,, Maybe there isn't enough current path through the stereos memory circuit to energize the relays coil.
It just doesn't seem right to me. I would sooner tap the 12V to cig' lighter well.
As for the temp gauge, both thermal gauges are supplied by the same inst' voltage limiter whether its inside the fuel gauge or plugged into the backside of inst' panel. If that limiter doesn't function, neither gauge functions.