Bayonet shifter - won't give!
Also, try pushing straight down on the shifter handle when inserting the feeler gauge, then up, wiggle, up and down. You do have to work it in there. I just checked mine, the tang that you are trying to push back isn't much thicker than the feeler gauge that you are using. May help to not push the feeler gauge in vertically, clock it a little to widen your spread. You may not definitely feel the release, keep working both the feeler gauge in and up and down with the handle.
Also, try pushing straight down on the shifter handle when inserting the feeler gauge, then up, wiggle, up and down. You do have to work it in there. I just checked mine, the tang that you are trying to push back isn't much thicker than the feeler gauge that you are using. May help to not push the feeler gauge in vertically, clock it a little to widen your spread. You may not definitely feel the release, keep working both the feeler gauge in and up and down with the handle.
