The closest I can think of is "train/trained/training"

For instance, it seems with grape vines if you cut off any new growth
and have a "clean" main trunk after a couple of seasons it stops
trying to put out new growth there.

Is there a technical/scientific term for this?

Now mesquite trees, especially ones that get a lot of water, they seem
to always be bursting forth with new growth all over the place. Trim
or pinch off emerging growth but that spot will still send out new
growth.

Is there a technical/scientific term for this?

Thanks

Jay