My E-type had electronic ignition on it when I bought it so I do not know much about the points set up on them. However I used to statically time my 70's Chevys with points by rotating the timing mark on the crankshaft pulley to the proper number and then rotate the distributor until the points open and spark. Could you do the same thing on the E-Type to time it and check that you have power at the points ?
You also might check that the ignition switch and wiring are all in good shape. Several years ago my ignition switch fried taking out some of the wiring going thru the tach to the coil. My impression of the original ignition switch is they were not the best quality.
David Barnes
68 E-Type FHC