Could you post a picture of your F2 from the front?
I have an F2A (F2 with DP-11 finder) and there is not a bar that will engage the rabbit ears. It sounds more like you have a DP-1 (No white A printed on the front of the finder).
Also, I'm not sure if you know, but every F2 is the same body. There is no Ai and Non-Ai body. It is the finder that is different. There are certain finders that will meter with only Ai lenses (like the DP-11 and DP-12 if I'm not mistaken, I have a DP-11). These finders do not have the small pin that will fit into the rabbit ears of the lenses. Instead it has a small indexing tab that will hang down concentrically with the lens mount. If you want to use a non-ai lens with one of these you need to push this tab up and out of the way and then you can meter using stop-down metering.
The DP-1, DP-2, and DP-3 were made for Non-Ai lenses and have the small bars that will fit into the rabbit ears. However, these will meter with any lens that has the rabbit ears, ai or non-ai. The only issue you will run into is if you are using an E-series lens or other lens without the rabbit ears. In that case you will need to use stop down metering.
If you pop the finder off the body, below the eyepiece mount on the finder you should be able to read what model the finder is. Let us know what you find out.