Put a volume gate on the music and take the output from the Morse Code to its sidechain input. Then mute the Morse in your track. That should give you music only playing when there’s signal coming from the Morse.

Edit: this basic technique can be used to do ALL KINDS of fun stuff. You know the dubstep wobble? Send an LFO (low-frequency oscillator, it basically just defines whatever wave you want) to the low-pass envelope filter’s sidechain on your synth. What you’re doing is:

• taking the synth you want to modulate

• making a sine wave on the LFO and playing with the frequency - quarter notes, triplets, whatever. You can automate this knob in your track in most DAWs.

• telling the LFO to control a low-pass filter on the synth - everything below the filter’s set frequency gets sent through to master, everything above it gets cut off. A high-pass filter does the opposite - it allows high frequencies through.

Now you play with LFO frequency to make fun wubwubs

What software are you using?

To achieve this you need to use a gate effect that supports sidechain on the music track, and then feed the morse code output into the sidechain input on the gate.

This tutorial I found with a quick search looks fairly comprehensive: https://www.practical-music-production.com/sidechain/

You could always manually edit the waveform if using a gate doesn’t work out for you.