I tried doing both and could not make it work. The full time job always took priority, and my search momentum suffered. There is just too much outreach, follow up, and mental bandwidth required. I ended up quitting and doing consulting instead so I could control my schedule while still earning income. For me, there was no way to seriously search while holding a demanding job.

I'm in the same boat, amfulltime consultant. As an self funded searcher further along in my career and life (family + kids), searching fulltime is not an option. I've given myself grace, recognizing my search journey is going to be longer. I've been on the hunt for ~3 years, with only half that time in real active state given competitng obligations, but I'm determined. History shows anything I put my mind to, I make happen...just a bit slower for this aspiration though, for me. Good luck!