I have recently acquired a 1987 Sure Lites LM-1 emergency light that is in wonderful condition except it doesn't work! Through testing I have determined the problem to be an open primary in the mains transformer, does anybody have a functional example they could measure the output voltage of, or any information that would help source a compatible replacement? The transformer has a center tap on the secondary, and each side of it measures about 15 ohms. I don't mind if it isn't physically the same as long as the output configuration is compatible with the existing charger circuit of the light.
Thank you for any info you may have!!

Is the transformer visibly burned?

Modern transformers often include one-time thermal fuse inside which may be blown for whatever reason. Transformer itself may be blown as well or not. If no other means to find out proper output voltage left, you can try to find this thermal fuse device, typically a small rectangle or cylinder, short it and power up the transformer briefly. Use some means of current limiting like a large lightbulb in series or a circuit breaker to limit possible fireworks

There is no burning, discoloration, or any other signs of distress on the transformer oddly enough, it just measures completely open across all the taps on the primary (it has a 277 volt tap). I'll peel the paper off of it later to see if there's a fuse present, or if any of the internal splices have been damaged.

It could be it overheated and the thermal fuse tripped.
What transformer is there, couldn't it use some generic one?
Detailed schematic or pictures of the board and noted connections could help so we may extract what transformer spec will work there...

An update for this:

I finally got around to desoldering and opening the mains transformer, there is no thermal fuse, although I found the cause of the failure. The common (neutral) connection of the transformer burnt away where is enters the bobbin, leaving a tiny stub sticking up, and a ball of melted copper on the bit of wire leading into the splice.

I'm not exactly sure what would've caused that while leaving the rest of the windings unaffected. Not much hope for making it work again for determining the output unless I can somehow find a way to get a wire to the tiny stub in the center of the transformer...

If there was a copper ball on it, it means there is short circuit among the primary and the thin wire just acted as a fuse. I doubt the transformer would be salvageable with that.
But I'm convinced it should be possible to replace it by some standard, run-off-the-mill type...

Yeah, there is also a likelihood that somebody put it 277 on the 120 volt tap accidentally and blew it up that way.

I assumed something generic should be able to take the place of that, my main issue is I have no clue what the output voltage of the old one was.

If we manage to reverse engineer the circuit, I think we may be able to figure that out...
And I wrote "we" intentionally, as to be able to help. I would need at least detailed photos or even better if you will be able to trace the circuit...
I hope it is composed just from basic components, not any proprietary or strange IC's...

I have just finished tracing out the circuit within the unit, and luckily, all of the parts are documented except for a TO92 device that controls the SCR in the battery charging portion of the circuit.

It appears that the six volt SLA battery is charged directly from one half of the tapped battery through the SCR, so presumably the output voltage of the transformer would have to be somewhat similar to that?...

I have attached a picture of my (roughly) drawn schematic for reference.

Then the transformer would likely be 2x6V.

The battery is charged with the transformer internal resistance as the only current limiting element, with a thyristor and diode in series (the circuit seems to not be redrawn correctly, probably some component terminal swapped or so, but it is showing well how the charging is handled).
With 2x6V charging current will be about 60% of the transformer rating (that indirectly tells what the internal resistance will be - typical OCV of such small transformers is 1.4x the nominal output at nominal mains input) when the battery is discharged (~5.5V), 40% of the transformer rated current when the battery approaches the full charge (6.85V; but it is not there yet, so the thyristor is firing) with mains at its nominal voltage.
With 5% mains undervoltage the currents will be 50% for discharged and 25% when near fully charged.
These figures sounds quite right - reasonable charging rate even at mild mains undervoltage and not overloading the transformer (giving room for some mains overvoltage), whilde at quite a common rated voltage level...

Generally these things use to not be that picky about exact secondary voltage - the minimum will be the 2x6V, 2x7.5V will give a bit faster charging, but may overload the transformer at high mains tolerance and empty battery, but it usually does not spend that long at that state (normally it is just maintaining charge, so the thyristor is firing really just occassionally), so it won't accumulate that much wear related to the high temperature.