is it safe to assume that prior to flat battery, you had the left speakers work as designed?

the flat battery is first culprit.
playing around the plugs with your spare tire may have contributed to problem, the radio has a BIG square plug that has smaller plugs as part of the bigger plug - check the individual pins, as they may have dislodged and make a poor contact...

the fact that the sound fades in and out suggest something electronic within the radio module...

check the battery voltage - check using the onboard computer by unlocking the onboard test functions - test #9...

there are plenty of threads on the battery and voltage checking, how to check the voltage cold, how to remove the surface voltage, then check it under load...

when baterry is less than perfect, a lot of STRANGE electronic gremlins come up, like windows roll up/down on their own, one headlight turn on/off, radio go mute, wipers start going off...

check the battery first...