Well, I would want to sort out what's up with the warning lights before replacing the box. It sounds to me as though the previous owner (or his mechanic) has bolluxed up the wiring to at least some extent. That's probably not the direct problem, but I'd still want to get it sorted out.
The red light should come on, brightly, when you turn the key on with the engine not running. One side gets 12v from the ignition switch, the other side is wired to the generator 'D' terminal (so at this point the generator is serving as the ground for the light).
The green light should come on only when the turn signals are on, and it should blink with the turn signals. It gets it's power directly from the 3rd terminal on the flasher, and should have a ground wire to the ground point behind the instrument panel.
It almost sounds like your DPO has wired the two together somehow, so the flashing might be coming from the turn signal flasher somehow.
I would also use an ohmmeter to check the resistor inside the control box. Disconnect the wire from the F terminal, and connect the ohmmeter between F and D. You should initially see 1-2 ohms. Now open the VR contact by holding the armature down with your finger. The reading should rise to around 60 ohms.
At this point, I don't think there is any functional reason to choose the Lucar over the screw terminals. Go with whatever is easy, and/or suits any leanings you have towards originality. Note that those oversize Lucar terminals are a bit hard to find, you'll likely need to order them from one of the LBC suppliers.