USCF rules about clocks

Under USCF rules, can a player with the white pieces insist on using a clock that records the number of moves and automatically adds time after reaching a time control?

In an OTB tournament, my opponent's clock didn't have these abilities. (I knew about this issue before our game because I had overheard parts of a controversy between my opponent and another player in the previous round.) I offered to use my clock instead, but my opponent had the black pieces and wanted to use his clock. I didn't want to cause a problem, and I don't know the rules, so I agreed.

During the game, I needed to move quickly to make the control, but I kept notating so that I would know when we hit 40 moves. Sure enough, I blundered on my 40th move (going from +2 to -2 according to Stockfish), with 6 seconds on my clock. (I also lost several minutes earlier in the game because my time was running during my opponent's turn. He said that his clock sometimes doesn't work if you hit it too hard. I don't remember hitting the clock hard, but I guess I should have been paying closer attention.)

I should have used my time more efficiently, and my opponent did a good job of taking advantage of my mistake. Still, I'd like to know the rules in case I'm ever in a similar situation.

THe USCF website does say the following:

The Three Levels of Clocks

The USCF's rules specify three levels of preference for chess clocks:

1. Clocks with time delay are the most preferred type of equipment.
2. Mechanical clocks are the next most preferred clock.
3. Digital clocks without the time delay feature are the least preferred type of equipment.

When players have questions about what type of clock to use for a game, they should resolve the situation by referring to the three levels of clock preferences.

For example: Two players arrive at the board at the same time.

Player A has a digital clock with time delay feature.

Player B has a mechanical clock. Because Player A's clock is more preferred, he gets to use his clock for the game.

The player of the black pieces has his choice of equally preferred equipment. If both players have a digital clock with time delay feature, Black's choice will prevail.

Now if both of you had digital clocks with "a" time delay, then Black was really in the right about wanting to use HIS clock, unless you could prove that it was defective prior to the game.

Thanks, Shivsky. Is there anything in the rules about what constitutes a defect with the clock and what to do when one player claims that a clock is defective?

As a former USCF club TD, I've pretty much had it easy => Ruling digitals over analogs based on a simple "Does it have time-delay" question as most of the tournaments in my part of the city seldom used  classical time controls.

I've never had to deal with that specific 40-moves situation before ... though with regards to defects, I think any player has a right to stop the clock, summon a TD and ask for a clock inspection the minute they feel something's wrong. If the player didn't pay attention to the problem until a costly critical moment that already elapsed, it's really hard to show any give after the fact.

I agree. I never considered complaining after the game started, either to the TD or to my opponent. (I did complain to my wife, and I suppose posting here counts as complaining too.) If I'm ever in a similar situation, I'd wonder whether the complete rules provide any basis for objecting to the TD before the game.