Layden makes some good points. The lamps appear to be Solar brand however the nut holding the door closed has been replaced with a simple hex nut. the original was a knurled round nut and would have had the identifying info on it that Layden suggested.
Inside the lamp, the back framework that would have held an asbestos pad and the reflecting mirror appears to be in place but the burner assembly itself should be adjustable, forward and back, in order to provide for an ideal flame shape that is reflected. That would require a couple of small slots along side the larger slot where the burner assembly fits to permit such adjustment. Once that fitting is properly adjusted it is secured in place with a couple of small screws through the base of the lamp. No adjustment slots for such screws seem to exist on these lamps.
the big issue is indeed, the bonnet on top seems to be purely decorative. There would be a large opening from inside the lamp to allow heat from the burners flame to escape into the vented top.
I too am convinced early electric lamps have been modified for some purpose. Whether it's early "restoration" or some attempt to make up a pair of lamps for a studio prop or carnival rode I have no idea.
These lamps were originally available as aftermarket items and could be purchased to install on whatever vehicle they were needed on. As they are, they should be considered parts donors.
Terry