How effective is a pharmacy-bought night guard for bruxism?

Not very: The over the counter mouth guard/night guard does not adapt very well to a patients mouth and therefore do not fit well. If they don't fit well it will be uncomfortable and you wont wear it as you should. You are much better off investing in a custom made night guard made by your dentist.

Mediocre at best: They are not custom fit, they are likely to be a bit soft and chewy and like an athletic mouth guard they can be chewed through easily. If you are a light bruxer you may be fine but more likely you would benefit from a custom fit firm durable appliance made by your dentist.

May make it worse...: Sometimes people who clench and grind their teeth at night can actually make the problem worse with an otc nightguard. Many of these appliances are softer. Generally speaking, when you put something soft/chewy in your mouth, it's to eat it...So you chew. When you go to sleep with something chewy in your mouth, the natural reaction is to chew...All night long...And wake up with bad TMJ pain.