Board Game Arena

To be brief: When you tuck the only card (which is obviously the top card) of a pile, it does not make any difference, BUT IT COUNTS.
https://boardgamearena.com/gamereview?table=348036027

At Step 139, I executed the dogma of <9 Wristwatch>, the effect went as follow:
1.[echo effect] I tucked <3 Almanac>, which is the only card of the blue pile;
2.[dogma effect] I tucked 4 cards by the effect because I have 4 bonuses on my board;
then I executed the card again.
3.[echo effect] I tucked <3 Almanac>, and right after that moment I claimed <Monument>.

In conclusion. Although the act of tucking may not change the game state, it still counts.
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The effects of <9 Wristwatch> is attached below:

<echo> Take a non-yellow top card from your board and tuck it.
<Factory> For each visible bonus on your board, draw and tuck a card of that value, in ascending order.

That's how I too would interpret it. You still tucked the card, even though the game state afterward was no different from how it would have been had you not done so. In physical play, while most likely you would just do nothing, you'd be perfectly entitled to pick up the card and "tuck" it by putting it back on its (temporarily empty) pile. It definitely still counts as a tuck for Monument - in my opinion, anyway.

Oh I like the "pick up" part! It is definitely reasonable than "shuffle the top card to the bottom" because it still works in one-card case.