Is there an app to simulate repeating clicking of a button in another app?

Assume I have an app, "Target," that I have launched and configured for a particular need (possibly different every time). Once Target is running and configured, I want another app (call it "Automate"; I don't know if it exists, or is even possible to create) to simulate clicking a button on Target's last active screen, repeatedly. The simplest "Automate" would do the click at a single programmed interval for a single programmed number of times, for example once a minute for 10 times. I would program both numbers before telling "Automate" to begin. A more complex "Automate" would read a script from a text file that might specify more complex timing, such as (for example), do the action five times at 30 second intervals, then wait two minutes, then do the action six more times at 45 second intervals, etc.

Does anything like the "Automate" app I am imagining exist on iPhone? I have looked at Shortcuts, but can't see a way to get it to click on the screen of another app.

TIA,

Mark

(as of posting, running iOS 15.1)