@srol
so, the primary reason that vocal improv can be easier for people than instrumental improv is that there’s no translation layer where you need to “know” the key signature and the chord changes, because you can tune the voice to the sounds around it without having to think about frequencies and note names and such.
that’s generally harder on an instrument because you have to think about what key y’all are in and what chord you’re on and what that chord is built out of and then figure out where in your line you are and where you’re trying to go and doing all that nonsense in real time just ain’t possible.
the key, in my estimation and based on the training I’ve received along the way, is to sidestep keys and chords and instead internalize the intervals involved instead. any given melodic line is a series of intervals and timings, so if you can make the intervals the core component you can absolutely process that in real time a lot more easily.
generally, it’s an easier technique to develop using a non-wind instrument like a piano or a guitar because that allows you to both sing the interval you’d want to go into your melodic line and play it at the same time, to start to tie the vocal interval you’re singing to the muscle memory of that movement on the instrument. you’ll often see jazz pianists and jazz guitar players that’ll sing their way through solos, and this is why (again imo).
doing the same thing on a wind instrument is harder (I do not recommend trying to incorporate throat singing into your trumpet improv but I am also not a cop). I found that it was easier for me to sing a short lick and then translate it to the horn to reinforce the interval practice and training my inner ear to go straight to my fingers as a practice pattern, but it’s absolutely that: one of those things you’ve just gotta practice until your face falls off.
but yeah: intervals, both getting to identify particular sound of particular intervals by ear (“hey, that’s a minor sixth” or “yo, nice tritone”) and arbitrarily hop around from note to a specific interval up/down on your instrument of choice, then reinforce with singing and playing lines either simultaneously or in call/response patterns, over and over again. that’s how I was taught the parts I was taught, anyway. hope some of it makes sense and helps on your journey!