I think I can take a better stab at it, but apologies ahead of time if it seems jumbled.

At night, the atmospheric profile -- including the near-surface profile -- is relatively moist due to the lack of daytime heating. At night, generally temperatures fall to the dewpoint; this is no different in the tropics. Tropical convection inherently does not depend upon CAPE (convective available potential energy), which is at a maximum during the day due to daytime heating; this is why you see a convective maximum late in the afternoon over land. With a moister profile through the atmosphere and given sufficient forcing for rising motion -- in the tropics, generally from converging winds at low levels in association with a tropical wave or the ITCZ...or even a tropical cyclone -- convection is more likely to be at its maximum just before the sun comes up. It also helps, particularly for tropical cyclones, that at or just after nightfall, SSTs are at a relative maximum for the day. At that time, convection/tropical systems can tap into the increased surface heat and moisture energy, something that continues through the night in conjunction with the aforementioned moisture profile, allowing for increased development.