See this site:
ENGLISH PAGE - Modal Verb Tutorial
I'd like to know more about Modal Past.
I couldn't find anything online and I've been having doubts about it.
Some grammarians give these examples for the modal past: should have, could have, might have, must have, etc +past participle (as in “it must have been in a fit of madness that President Bush developed or reinforced the idea for NCLB”)
Others (the majority) call this form the modal past perfect(ive). In which case the modal past would be the past forms of the modals can (=could), will (=would), may (=might) etc.
Which do you think it could be?