Delayed start on turning key - '91 Toyota Corolla

Check the battery terminals to make sure they’re clean and tight. If there’s a bad connection at the battery, and you turn the key to the start position, the current required to turn the starter can’t pass thru the bad connection. But if you hold the key in start position, this bad connection will begin to build up heat from the current trying to pass thru it. This heat can then cause the battery post to expand slightly to where a good connection is made and the engine starts.

Tester