There is an imaginary mirror dividing the stage in half. You are a boy scout, and another boy scout is your reflection. Your reflection has to be your same size and weight for some of this to work, but they don't need to look like you. It's obvious to the audience that there are two of you and one is pretending to be the reflection of the other. They'll watch for how close to perfect you manage to do it, that's the point of this skit. Practice beforehand and do try to be perfect.
You, a boy scout, come towards the audience, sockless, buttoning your shirt. Another boy scout, your reflection: dressed the same, doing the same steps as you but mirror image. You two are walking toward the audience but angling closer, towards the front center stage.
You notice your reflection in the mirror, face it, adjust your collar. Close your eyes, yawn, stretch. You're waking up: wiggle your jaw back and forth, rub your eyes, scratch your head, stretch your back back, scratch your butt.
Then you get socks, then lean back against the mirror (back to back supported by your reflection) and put your socks on standing up. (Here's where a bench might be useful, but it's a better trick if you can do without it.)
Turn around again. Make funny faces in the mirror. Stick your tongue out, say "aaaaah", look down your throat. Try to look up your nostrils. Notice a pimple on the side of your nose, look real close with one eye, stretch the skin by your nose, try to pop the pimple.
Stretch again, draw hand over your face, trying to wake up. With your hands stretched over your head, lean against the mirror (fingertips to fingertips supported by your reflection). Stretch the legs. Try to lean one-handed and stretch the other arm.
Stand again, comb hair. Sing to yourself a line or two, "somewhere over the rainbow", just warming your voice up. The reflection can sing it in unison or harmony. Straighten collar. Do a cheesy grin, standing up straight, look debonair. Wiggle eyebrows suggestively.
Walk away from the mirror, but spin around and do a pose pointing at your reflection.
Walk away, turn an imaginary doorknob to go out the door.
Change your mind, go back. Feel the borders of the mirror. Pick up the mirror (interlock fingers with the reflection) and carry it with you offstage. If you can, carry it on your back (carrying the reflection on your back, back to back, still interlocked fingers where you both are gripping the mirror, with them doing steps in the air). If you can't pick them up, just carry the mirror on the side, so the mirror is facing the audience, and you and the reflection both walk offstage. The reflection will have to break symmetry to walk around when you turn the mirror to face the audience, you should both step but rotation not mirror image to do that.
Afterward go back for bows, where you both bow in mirror-image fashion, ham up the bowing in mirror image fashion, then exit on opposite sides of the stage.
(The punchline is actually the bowing at the end, where the two actors are no longer pretending to be mirror images, but act like mirror images anyhow.)
I just made this up. I put it on reddit r/WritingPrompts (responding to my own prompt) before I put it here. If anyone actually performs it, please tell me how it went, or even better put up a youtube video of it. Groucho Marx in "Duck Soup" had a similar skit, but it differed in that he suspected the mirror wasn't real.