Add electrical box to existing ceiling
With most brackets, there is an easy-to-find specification for the range of spacing between the joists.  Alas, Saf-T-Brace does not publish one I could find, though Home Depot says it is for 16 to 24 inch joist spacing.

If the joist spacing (gap) is more than about 12 inches, you might be able to shorten the braces to fit, however spacings less than 14.5 inches seem to be a specialty item.

I checked dozens of hardware and electrical suppliers and finally found this one which adapts to 8 to 16 inch spacing:



Platt has a slight presence in your area; alas it likely a 50 mile drive for you to go get&mdash;either Fremont or San Rafael.