Okay fair enough, I agree they aren't entirely random lol, but they for sure are not recent/recently closed/most used/any classification heuristic I can think of. Maybe its 'most recent but with a few exceptions' ?
I may be misunderstanding what exactly SwitcherMod is doing. I'm using it with the intent of having the close button always being visible. I attempted to turn off all other features. What the heck does "Inactive Recent Icons Alpha %" mean?!?!? And for the "recent app icons" setting, which option denotes the typical iPad's behavior; "remove" or "normal"? Now, before you say anything, I realize "normal" seems like the obvious answer, but I was thinking "remove" was talking about removing an extra feature in SwitcherMod that was otherwise not a stock feature and that "normal" was SwitcherMod's default behavior which would be different from stock behavior. Kinda like double negatives... Aghhh.... Lol. Regardless, neither seem to behave consistently on my device. I guess I'll try a reinstall...
You've got the interpretation of the setting wrong, and that's probably where your problems stem from.
Recent App Icons (in your scenario) should be set to "normal". That means recently used apps are handled as normal by the switcher. In other words, they appear in there.
Setting it to "remove" will, funnily enough, remove the recent apps from the switcher. That is not "normal" behaviour for an iPad. See how that works?
As a general rule, tweaks rarely come with lots of settings which you are forced to turn OFF before you get started. Most settings are optional extras which you have to specifically turn ON.
A "recent app" is any app which has been previously opened but which is no longer in memory. When your run out of free memory on the iPad, the OS will dump the one which has not been used for longest (at the end of the list) from RAM and make it a "recent" app, which is in essence just a shortcut to launch the app from scratch again.
Ever wonder why your switcher is empty when you respring? It shouldn't be empty as standard. It's because you have set this option to "remove". That's probably also why you are not getting on well with your other problem related to passcodes and respringing!
Set the option to "normal" and then check the switcher app list. You will see lots of apps in there.
That is the list which the multitasking swipe gesture is using, and that is why you have seemingly random apps coming up. If you really want to clear out the switcher, just remove all the apps from it by pressing their "x".
I suspect after this change, you might not think that the respring to reset your passcode lock timer is so tedious since all your previously open apps will still be present in the switcher!