I wish you well with this quest. To the best of my recollection games were not routinely filmed until circa '88/'89 season. Until then we had to rely on the BBC / ITV, therefore there may only be footage of perhaps three or four games per season during Garner' s first decade playing for us - '78-'88. Of course he didn't necessarily score in those filmed games although I always thought he turned it on a little for the cameras
This lack of footage is a great pity. His five against Derby and his four against Sunderland (?) weren't recorded to the best of my knowledge. I certainly haven't seen them since. So many of his wonderful finishes sadly only exist in the memory bank.
I don't remember a Garner hat trick against Burnley although he generally scored when we played them, including two penalties in one game if I recall correctly.
YouTube has a number of his goals, perhaps thirty or so. His great goal against Liverpool in the FA cup '83 was recorded but I haven't seen it on YouTube.
The Elton Welsby fronted 'Kick Off' magazine show in the late 80's showed all his goals, which would amount to forty or so in his final four seasons between '88-'92. I would wager about another thirty or forty across the rest of his career at Rovers were filmed so probably close to eighty goals in total have existed on video at one time or another.
It can be fruitful searching YouTube for other clubs. For example, a Garner goal away at Swindon in '84 in the FA cup is on there. I went to that game so it was nice to see it again recently.
If anyone has footage on video of Rovers matches that aren't on YouTube I am happy to convert them and publish it for all of us to enjoy. I live locally but have limited time so only really want to commit to videos from the '70's/'80's.