What are the rules regarding play of a singleton?
Let's look at the relevant Bridge Laws.
Law 16B1 says:

Any extraneous information from partner that might suggest a call or play is unauthorized.This includes remarks, questions, replies to questions, unexpected alerts or failures to alert, unmistakable hesitation, unwonted speed, special emphasis, tone, gesture, movement or mannerism.


(a) A player may not choose a call or play that is demonstrably suggested over another by unauthorized information if the other call or play is a logical alternative.

Law 73D1 says:

It is desirable, though not always required, for players to maintain steady tempo and
unvarying manner. However, players should be particularly careful when variations may
work to the benefit of their side.

Law 73D2 says:

A player may not attempt to mislead an opponent by means of a question, remark
or gesture; by the haste or hesitancy of a call or play (as in hesitating before playing a singleton); by the manner in which a call or play is made; or by any purposeful deviation from correct procedure (see also Law 73E2).

Law 73E2 says:

If the Director determines that an innocent player has drawn a false inference from a question, remark, manner, tempo or the like, of an opponent who has no demonstrable bridge reason for the action, and who could have been aware, at the time of the action, that it could work to his benefit, the Director shall award an adjusted score

Law 74A2 says:

A player should carefully avoid any remark or extraneous action that might cause annoyance or embarrassment to another player or might interfere with the enjoyment of the game

Law 74C prohibits &quot;violations of procedure&quot; including 74C7:

varying the normal tempo of bidding or play for the purpose of disconcerting an opponent

The above are all from the most recent (2017) Laws of Duplicate Bridge. All boldface is my addition. The laws for contract bridge are very similar except for mentions of a director.
All club and tournament games have time limits for each round. So do all online games that I know of.  A three minute hesitation in play, especially when holding a singleton of the suit led (not at trick 1, when there might be a need to plan the play) is very much longer than usual, and would usually be considered quite improper. A director or club management would have discretion whether to take action. It would be normal to ask, after the hand is over, what reason there was for the delay. If there was not a good reason, the player might be warned, or even removed from the game or barred from the club or event. A warning would be usual for a first offense. If damage seems to have been done, an adjusted score would be awarded.
Note, however, that such action is only &quot;unethical&quot; if it is done with intent to secure an advantage or disconcert or annoy opponents. If the player was belatedly trying to plan the defense, that is not unethical, although 3 minutes is excessive.
Online and tournament timing is usually 7-8 minutes per hand, including the auction, with the time limit applied only at the end of the round, often 2 or 3 hands, although it may be as few as one or as many as 5 or more hands long. Club play time varies widely, but many clubs use a rough figure of 7 1/2 minutes per hand. Online &quot;speedball&quot; events are typically 15 minutes for three hands.