There are plastic caps that come in power window kits. Visit a audio/alarm and accessory shop, they may have extra caps they can give you.
The assorted caps are in the top left of the picture;
nothing a cut-off wheel can’t fix
It’s fun just to browse through the hardware store to see what they have. Good ones, or the big box will have all kinds of plugs, or try a woodworker supply store. Use a little imagination and may have to color to match. For some reason all the old gear was left in place which complicates the issue. So maybe have to use two plugs-one for the big hole, then drill for a second one piggy backed to allow for the stud of the old mechanism protruding. Hard to tell if its flush or not which I think it is so not much of a problem.