The construction “mayhap it happens” followed by the infinitive is awful. A better construction would be “mayhap it” followed by the third-person singular indicative or subjunctive. “Mayhap it rains” or “mayhap it rain” or if you want to puff it up “mayhap it doth rain”.
(But the use of expletive pronouns usually a bit silly. “mayhap rain falls” does the job nicely.)