Might as well pull the cooler line. All the work to put ATF in is the same.
Bit of a pain but IMO the worst looking oil is on the bottom of the pan, and won't drain out. Worth the effort to drop and wipe out. Filter is a strainer and shouldn't need to be touched. There is some DIY's elsewhere on the web, showing what line on the cooler to pull.
While I thought it a pain it really isn't that bad. I forget, I think I did mine cold. Remove fill plug first. Snake a 5/8" (?) PVC hose down from engine bay, shove in a funnel. Drain pan, drop pan, clean pan, reinstall. Fill with x quarts. Pull cooler inlet line, drop into a marked container (like an empty Maxlife container?). I don't know if I would want to drain more than a quart at a time. I think it's a minute of run time on the engine to get a quart? Repeat until what, 8 quarts? comes out. Take for short spin to get ATF up to temp--the DIY's show how to get the dash to indicate proper temp, but I have a Scanguage and used that. Park on level ground, leave engine running, pull check bolt. If none comes out, pull fill plug, add more. For topping off I bought one of those hand pumps that goes into a quart bottle to lift oil up and in.
I'd go find a good DIY on the Tundra forums, a good one will have pics and whatnot.
Edit: I used Maxlife also and it seems fine. Granted I don't tow. But I changed the OEM fluid at 80k and it looked a bit dark; 60k later and last time I looked it was still red.