sounds like its all fun & games.. so how come you have the power hooked up to an indicator if there was already a power lead there?
if i'm following you correctly, then the yellow in the gem is power, the red in the gem is accesories, which would mean that, the red on the new tape player would connect to the yellow on the gem & the yellow on the tape deck connects to the red on the gem??
one thing you could do, is locate the fuse box, there will be fuses for things that work on accesories, and fuses that work for things when the engine is running, hook up the wires on your tape deck to a corresponding fuse ('on' & 'acc')