I'd strongly suspect your brainbox, and check the connexions on the rest of
the electrical system. As we've seen, it only takes one dodgy wire to make
the whole thing fall apart. Double-check the ground on the coil, the
ignition circuit wiring, and finally, that dueced brainbox.
Seems to me from your description that you car is just not a morning person.
Seriously, it's probably colder in the morning, and metal bits, particularly
small electrical ones, do expand and contract a bit with changes in outside
temp. If you've got a bad connexion someplace, and it's just a bit off
making contact, the temperature change might make a difference. I'm sort of
grasping at straws there, but who knows? It could happen.
75 MGB 'Rags'