Hickok45 has a couple of videos in the Savage 99. One includes disassembly and cleaning. Both are very informative and should give you what you need.

https://www.youtube.com/watch?v=PKXn-x1GEHE

I have a pair of Savage 99's both in .308 and 1957 vintage. One is a 99F. Found the pair of them six months apart after a 25 year search. Great guns that both shoot exceptionally well. More affirmation of Savage's reputation for accuracy.

PF