Honestly, MOST patent attorneys are not going to be terribly interested in working for equity as their sole or primary payment method. More precisely, most patent attorneys that are any good won't be very interested. Why?
1. Most good patent attorneys are very busy. There is lots of available work from large clients that pay. Maybe not always pay well...but pay.
2. Most good patent attorneys have seen/heard plenty of song-and-dance from cash-poor but self-hyped start-ups. They tend to be wary of spin and want to see the money as a way of knowing that others believe in the company enough to invest.
3. Most patent attorneys have poor social and business skills. They are unable to recognize good opportunities that are out of the norm. Their expertise is in legal and tech. So, they just want to paid for the work.
I am a patent attorney that, in recent years, has made several deals with start-ups. Typically, those deals involve some combination of cash and equity. The exact proportion of cash/equity varies based upon how convinced I was in the combo of the biz ability of the founders, the disruptiveness of the invention, and market potential.
You can probably find a patent attorney like me. They will tend to be very experienced. But they have grown tired of working for the big corporate tech behemoths. Instead, they want to help new companies get their start. But they are hard to find.