Are they both fed from the same fuse?
I think you need to recheck your meter readings.
Unless you have a 24 volt system, maybe you didn't make good connection with your meter probes.
Place the meter on resistance, put one lead on the small battery post, the other on the case of the amp, meter should read somewhere around .3 ohms.
If that is close, put the meter on DV voltage scale, connect red lead to large battery post, put black probe on the power wire at the amp. If you read voltage you have a problem on the power side. If no voltage is there then Life is good. While you are still connected to the battery, put the probe on the amp remote terminal, If you read voltage then it is in the remote circuit.
I am suspecting the light and stereo are either unrelated, or it will be a power problem.
Good luck.