On most Model 3s, the "T" logo lights up and blinks for a while when charging begins, but then goes away after a while (a minute? Five minutes? I'm not sure how long). It sounds like there's something wrong with yours, but it's not exactly a high-priority repair. If I were you, I'd either wait until the next scheduled maintenance to have it fixed for see if a mobile service visit might be able to fix it; I wouldn't bother taking it in to handle this exact problem.