A bright light works but any salient information is an "It depends" answer:
How dark is the area where the test subject is?
How long have their eyes had to get adjusted?
What color is your disorienting light?
Is the test subject colorblind?
Is the source constant, high rate pulsing or flashing?
If flashing is it at a PSE (photo sensitive epilepsy) rate or other disorienting rate/pattern?
Are one or both eyes affected?
Etc, etc.
So, with those few questions in mind:
If the area is relatively bright dazzling lights are less effective.
An inexpensive 100 lumen light will temporarily blind a sleeper you just woke up but not a dark sunglassed guy on a bright beach.
If the test subject has been in a dark room for a while then gets hit with the dazzler they will likely be more greatly affected.
Some colors are much more effective than others, including better than white light. Some sequences of certain colors are even more effective.
Colorblindness may be at least a partial defense. DHS built a "maglite" sized high powered dazzler several years ago, and allowed volunteers to test it at a trade show. I talked with the project manager during the demos and watched ~ dozen testers, as my employer was interested in the technology. Most started to be nauseated or disoriented in 15-30 seconds. One colorblind subject had no effects after 2 minutes, including the last minute of having the device about 4 inches from his face. The project manager stopped the test officially for safety reasons, but later indicated that colorblind people seemed to 'skew' the results of the effectiveness of their testing.
(He did make the point that a bright light was no where nearly as effective as the patterns. )
The flashing pattern and colors can make all the difference in the world, forcing the test subject to turn or close their eyes.
Some patterns are more effective when only viewable by one eye.
Spectrum can also make a difference: a moderate powered IR solid state laser can instaneously make a test subject experience significant eye pain / headache without an overt reason, potentially taking them out of the fight. Higher power devices could make that instaneously permanent.
So to answer more succinctly, I would submit that a carefully engineered and constructed dazzler may be much more effective than a firearm in disabling an opponent or gaining an advantage as you noted. Now all you need to do is go search for a rail mountable DIY dazzler to pick up that advantage