If you consider full time 40 hrs a week then I saw part time.....If you mean do I have a second job than the answer is no.
I am not in tree country so the majority of my sawing is small 1-5 log jobs. This means that there are alot of people who don't know a saw log from a tree and will put the entire tree on the ground to be milled

my demographic for the most part are artisans who want special small quanity wood.
I have three other "portable" mills within an hour of me that I know about. Two of them are part timmers and rarely saw, the third is a full timmer who is up in the mountains and he charges by the board foot because he is competeing with five stationary mills that do. He is portable, but only travels within a few mile radius of his location.
The biggest reason I went to hourly is because around here you can say " I will need help loading and off loading the mill" and everybody says "okay, no Problem" and 15 minutes into the job I am alone and all the help found other things to be done...... So I switched to hourly and now the help stays around.
It's hard to break old habits, but I think that the days of sawing by the BF are soon gone..... The oldtimers who have used stationary and portable mills in the past balk at the idea, but the younger generations don't even flinch.
I think just from talking to other sawyers online and at shows that the majority of full timers have made the switch..... there are the holdouts, but especially out in the northwest part of the country most are hourly now.