Stage direction like "Enter Hamlet"

I'm wondering about the grammatical structure of a stage direction "Enter Hamlet". Is "Enter" in the imperative mood or the present subjunctive mood? If it is in the imperative mood, who is the person that receives the command? The actor who plays Hamlet or the director who directs the play?

Such stage directions are really a puzzle.

I wouldn't see "enter" as in "Enter Hamlet" as an imperative or a subjunctive. That makes no sense. Stage directions in Latin use normal indicative forms such as intrat, intrant, exit, exeunt. I should say "enter" in "Enter Hamlet" is an indicative form with the speciality that the third person singular has no -s, whatever may be the reason for this lack of -s.

I've had a look at the stage directions in act one, scene one of Hamlet on Shakespeare Online, and found:

Francisco at his post. Enter to him Bernardo
Enter Horatio and Marcellus
Exit
Enter Ghost
Exit Ghost
Re-enter Ghost
Cock crows
Exeunt.

Somehow it seems there is a strong influence of Latin stage directions. Sometimes we have the real Latin forms as in exeunt (they exit). Even the position of the person after the verb to put emphasis on the person who enters or exits may be seen as Latin influence. Nevertheless the lacking of -s is a curious thing.