Automating LFO presets?

The LFO device has these 1-6 buttons on the bottom right that you can right click to store an envelope (really convenient) and my question is simple: is there a way to automate choosing them? I’m making some trance gates and I would like to be able to just toggle which one I want to use instead of making multiple LFO’s and automating them all on and off. Usually right click will automate something but in this case it just stores the preset. And I don’t see anything showing up under automation to do this. So it LOOKS like you just can’t do it but I’m often wrong about these things.

(BTW if you can’t do this, it sure would be awesome if you could.)

Edit: Considering making multiple LFO’s of the “pieces” (long and short) and just one shotting them into the pattern.

Nopes, you can’t automate those.
You can add 6 LFO’s on your track and then simply shut down the profile you don’t need and enable the lfo with the profile you do need in the track. As a matter of fact, you can add any amount of LFO’s to your DSP rack and control them this way, you then have more than 6 profiles at your disposal.