Since we are in budgetville, I'd recommend the itp A series.
The A3 is the lightest, smallest one. 2.7 inches long or so and a half inch diameter. Youve got a 2, 18, 80 lumen mode. Between the 2 and 18, I think you are covered nicely.
I recommend using a L92 Energizer Ultimate Lithium. It is a 1.7 volt battery that gives a bit more brightness and is very long lasting at higher current draws. It doesnt leak either. Since this is a BACKUP, I recommend this. They have 15 year shelf life, and a 4 pack costs a whopping 5 bucks or so retail. They are easy to get, and are very lightweight.
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The itp A1 uses a CR123 and is shorter but a lot fatter. It has a 3,30,200 lumen mode. Since you dont need the 200 lumens, you may not want the extra weight. BUT, the CR123 has great energy density and will have great runtime.
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The itp A2 uses a AA. Longer than the A1 but slightly skinnier. I'd use the same Lithium primary battery for it.
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I think the itp A3 is the right mix of extreme light weight, smallness, quality build, and cheap cost to meet your needs. Runtime at low modes is going to be very good, more than enough for a backup light. If you have eneloops, go ahead and use them. But, since this is a backup light, I don't think that investing in them is a good idea at all. It is just not cost effective to get batteries and charger for a rarely used light, when primary lithiums are 4 for 5 bucks and are lighter weight, great runtime, no self discharge.