One common cause of this is a cooling system inadequately
purged of air. The EACV (or idle air control valve) is
cooled by the anti-freeze in your car's cooling system. That
valve is a high spot on certain cars. Follow the manual to
the letter on purging this system, and this may cure the
problem. Getting the fan to come on twice may take 40
minutes of idling, so have a magazine.

Other sensors that feed into the car's computer may also be
seeing inadequate cooling due to air in the system.

I had this problem at stops a couple years ago with my 91
Civic. Turns out I'd recently replaced the thermostat,
introducing plenty of air into the system, and had not done
a proper purge afterwards. A proper purge fixed the problem
right up.

Vacuum leaks like you say could also be behind this. Other
causes are possible as well. One step at a time...

Mine would bounce up and down between idle and 1500 (accord).  Mice had eaten a
hole in the air cleaner element replaced that and also cleaned the thortle body
very well.  between those two it solve it.