Yesterday I had a guy call up and tell me that he was 20 miles East of my airspace and wanted to transition. I've seen this a million times, another guy who wants to fly over the boneyard only this guy hadn't contacted Tucson approach prior and was just a primary target on radar. I asked if he was talking to approach and he replied that he was "under their airspace." [insert the screen shot of the little box on the sectional which states "contact Tucson approach on (freq) within 20 miles here] I typed him into the system and got a beacon code and asked him to squawk it. He acknowledged but he never came up on the scope. I verified that he got the code and he said that it was in the transponder. I asked if the transponder was on and in the ALT mode. He said yes. Now at this point he is either playing me and knows that he doesn't have a working transponder (why he didn't bother calling approach) or he has a transponder malfunction...not a big deal. He then got bold and asked if he could "orbit the boneyard"...aha, now we know for sure. I told him that he could fly over the boneyard but couldn't make more than a 180 degree turn (as per base regulation) and then he needed to leave. "That's perfect, I'll just fly over on my way to Marana." Meanwhile we have a medical helicopter that needed to be separated from him along with a lifeguard Air Commander coming from another direction, both had him in sight according to approach. At this point, I got curious and looked up his tail number and got his name and registration info. A Cessna 152 based out of Salt Lake City. To his credit, he continued NW to Marana and thanked me for letting him transition. I replied, "you're welcome [first name]" Long pause..."okay, you got me, how did you get my first name?" I replied in my best German accent, "Oh...vee haff vays." Side note: Found out later that the guy I relieved yesterday was exposed to the corona virus...schedule pending. He's quarantined.