I wouldn't hook the bulb up to just any 6 volt source, at least not one with more current available than 2 dl23s. I haven't measured the E2 but with the 6P, the 6-volt open circuit voltage drops to about 4 volts under the 1 amp load. I think ANY P60 bulb would test as burnt out if connected to a regulated lab supply set at 6 volts and capable or supplying a couple of amps, or, at least it would be burnt out less than a second later.
BTW, the B65 Ni-cad pack has an open-circuit voltage of 4.8 volts, as expected. But, under similar load, only drops to 4.2 volts. Thats why the 6R rechargeable light comes with the R60 bulb. In spite of information to the contrary, using the P60 bulb in a 6R will cause very short bulb life (like one hour or less). Just saw it happen last week. This may be related to the overnight charger for the 6R. The rapid charger may not have this problem.
Anyhow, test your bulb with an VOM or low current continuity checker.