One of the best lessons I learned playing background solo piano in Lounges and Piano Bars is, never stop the music. When you stop between songs or even pause, you give the audience reason to make requests. Usually the requests do not fit your style or you just don’t know the song. That puts you in a difficult spot especially when it happens a-lot. So I learned to Vamp or Fill time between songs with chords and improv material. Some of that style of playing helped my song writing ideas and enabled me to clear my head and think about what I was going to play next. Also, I could talk to the people sitting around the piano while playing. When I stopped playing it was, break time.
One of my first real jobs in music was at the Desert Inn in Columbus, Ohio in the early 60’s. I would park cars from 4pm to 6pm, change clothes, then play solo piano in the dining room from 7 to 9, then play at the piano bar from 9 to 1. Needless to say I had to memorize quite a bit of music to fill that much time. I played without music. The real lesson was, the different styles for each job. People eating vs people drinking. Sometimes I would play the same songs just change the tempo and style of playing. That is where the jazz style came in handy.
Funny story, I also remember the Fake Book guy that would visit me at the Inn to try to sell me Fake Books. It was like a drug deal back in the day. Everything was hush hush. Now you can buy them very legally at any music store.
Found out very early that playing a solo piano gig was much easier than playing in a band. Reason being, that you could add or subtract to a music arrangement with no problem. Also, if you forgot the B section of a song you could improvise or simply vamp to another song. And there is something to the fact that other people are counting on you so that adds to the anxiety factor. Kind of like team sports. I did prefer solo. Many years doing both I still prefer solo.