If it is an "install" disc, isn't it unnecessary to need to use an auto-swap feature anyways? At least when I use auto-swap it is for instances of there being 2 or more "play" discs.
That aside, maybe Forza 4 is just unique in that its discs have an install and a play component. If that's the case, make sure you have it set up as follows:
[Storage Device]/Games/Game Name/ disc 1/[ extract disc one here ]
[Storage Device]/Games/Game Name/ disc 2/[ extract disc two here ]
Make sure too that the folder names are "disc 1" and "disc 2" because otherwise the auto-swap won't pick it up. If you're using FSD like I do for auto-swap, make sure that the F3 plugin is enabled. Also, if you're using FSD's auto-swap you might need to disable Dashlaunch's auto-swap feature. Having both of them active sometimes causes issues IIRC.
Did a little bit of digging and turns out disk 2 (install disk) needs to be installed from the disk and not the dashboard. So, what you need to do is copy the proper files from it into the Content folder, or you could try launching the default xex on disk 2 and installing it the ordinary way. Though, whatever you do, auto-swapping won't be needed.