Why does my Brother labeler say both 9.5V and 12V?
First, the two voltages determine a range, not two separate operating voltages. Anything between the two voltages, such as 10.4 volts, will also work. Why 9.5 is specified is something of a mystery, since the Brother AC adapter recommended is only rated at 9 volts.

Also, I suspect your problem is quite simple - your 9 volt adapter either is not working, or your connector is the wrong polarity. For this purpose, the + voltage should be on the outer contact, and the inner should be the -.  It is also possible that your adapter simply does not provide enough current. The Brother AC adapter is rated for 1.6 amps, so if you're using something significantly wimpier than this, particularly since your voltage is at the bottom of the operating range, that it is being pulled down to the point that the unit doesn't operate.