man - just curious - are you sure that this bulb was made by Amglo? Could you post some detailed photos of the bulb? We would be very interested in seeing it since they are very scarce. My
Amglo Sheaffer's bulb does have a control box tethered to it but it's crudely made without any markings whatsoever. Furthermore I don't feel that it's a good candidate to gauge any electrical measurements from since the one time that I lit the bulb, it seemed to be overdriving it. Due to fear of damaging the bulb, I haven't used it since. Aside from powering the bulb, my control box also employs some type of primitive mechanism that causes the bulb to flash.
The John Gabel Manufacturing Company used an Amglo sign bulb in their 1930s Charme model jukebox. This is probably the most common Amglo sign bulb and I do see these jukeboxes come on the market from time to time. Your best bet may be to contact someone who has restored a Charme or someone who owns one. Surely there must be some good forums related to antique jukeboxes and restoration. Such a person may be able to supply you with the needed electrical data or perhaps an electrical schematic of the circuit that drives the tube in this jukebox. Bill Butterfield is one name from the Jukebox world that comes to mind who is familiar with this model, but I don't have any current contact information for him.
Even if such measurements could be made, I'm not stating they will be the same as what your bulb requires, but it would be a good starting point in understanding more about these bulbs. If you do learn more information then I do hope you return and share it with us!