There's nothing designed to do this by default, unfortunately. However, AMK does have some special music commands which can help. I'm not sure of the exact specifics of how they work so you'd probably have to play with them a bit, but the two commands in question are:
$F9 $XX $YY ; data send - sends two specific bytes $XX, $YY to the SNES when executed
$F4 $05 ; send position - sends the song's current position to the SNES when executed
Both of these send the specified data to the addresses labeled !SPCOutput1/!SPCOutput2 in the asm/SNES/patch.asm file (by default $7FB004/$7FB005). So you would just edit the song's TXT file to add one of these at the end of one of the channels before the loop, and then on the SNES side you just check the output for when that sends.
Here's someone else's post that gives an example, though with a different usecase there.
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