Along similar lines, I would want the woman doctor to feel flattered by my erection, but at the same time, considering me a perfect gentleman that wasn't trying to make anything happen with her. I would expect that she would want to remain professional, but nice to know she knew the ball was in her court if she wanted to pursue anything.
The closest i came to giving myself away was one of the first times the doctor felt my balls for lumps after the hernia check while lying on my back. The previous several years he examined me during the annual physical, he would only check for hernia. As i lie there on my back, I would be staring up at the ceiling, anticipating that soon after feeling around my abdomen, he'd lift up my underwear, maybe pull down a bit & do the hernia check only. So during a physical in later years, seemingly spontaneously after the hernia check, he ran his fingers over my balls to check for lumps. Staring at the ceiling & this never being done to me before, I didn't see it coming, I may as well have been wearing a blindfold. So when i felt this, it took me by surprise & felt good at the same time.
I don't remember if it was this first year or the next, when i may have been in some anticipation of this new thing, he briefly gently squeezed my balls. It happened too fast for me to get an erection, & I'm not attracted to men anyway. But the pleasurable effect caused me to be slow to sit up, to the point where he went to put his hand on my back to guide me up. Being about 30 at the time, that made me sit up quickly because I didn't want anyone helping me up at the time.