Choosing tense for reporting verbs in reported speech

“ARE there any rules prescribing when to use present-tense reporting verbs over past-tense reporting verbs? Also, can’t we just use past-tense reporting verbs at all times so that whatever is being reported can just be construed as an event in the past?”

These perplexing questions were posted in Jose Carillo’s English Forum recently by member Michael E. Galario, and I must admit that it took me quite sometime to figure out how to answer them with adequate instructive precision.