You may be seeing a reflection from the backside of the mirror! It may be a bright spot but that won't affect the reading of the test as it won't be in focus at the knife edge. I see a reflection on some of the mirrors that I test, the 12.5" porthole being the worst at the moment as the back surface is a nicely polished surface. The cast pyrex blanks tend not to produce a good reflection as the backside is usually fairly rough.
Make sure that you are at the ROC as best you can and then get the light from the frontside of the mirror to the knife edge. See if the light is going the same way as the KE moves (inside of ROC or the other direction (outside of ROC) and move the tester until it's tending to blank off the whole mirror at one time. At that point, you can start using the distance control on your tester to find the shape of the mirror. I might note that the reflection from the backside can be as bright as the light from the frontside of the mirror if the back is nicely polished.
Please note that I like to use a bright light to find out where the mirror is reflecting to and that also allows me to look at the reflection of the light and get the ROC to an approximate point as then the light will be in focus where it returns from the mirror.