Uninstall fails: Uninstaller placed in SysWOW64 (<System>), but registry points to system32

[sprob]

I'm installing a program into the <System> folder, and since I'm on Windows 10 64-bit the installer I built with InstallForge places all files in C:\Windows\SysWOW64, including the uninstaller EXE.

But when I go to Apps & Programs and try to launch the uninstaller, I get an error message stating "Could not find the file C:\Windows\System32\Uninstall.exe". Of course, that doesn't exist, because the uninstaller is in SysWOW64.

In fact, when I look in the Windows registry, specifically the key:
Computer\HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Microsoft\Windows\CurrentVersion\Uninstall\My Program

The keys DisplayIcon, InstallLocation and UninstallString all point to C:\Windows\System32 instead of C:\Windows\SysWOW64.

Why is that?

(Similar to this thread from 2016, I think.)