##Actually, 18 bytes

`♂l╔l;Y"[].⌂"£n=1`

Try it online! (calls the function with ƒ)

Explanation:

`♂l╔l;Y"[].⌂"£n=1`  push a function:
 ♂l                   map length over input
   ╔l                 uniquify
     ;Y               1 if list is empty else 0
       "[].⌂"£n       call this function that many times:
        [].             print an empty list
           ⌂            exit
               =1     1 if length of unique list equals 1 else 0

If the function-only requirement is lifted, the equivalent program works for 15 bytes:

♂l╔l;Y`[].⌂`n=1

Try it online!

Actually, 18 bytes

`♂l╔l;Y"[].⌂"£n=1`

Try it online! (calls the function with ƒ)

Explanation:

`♂l╔l;Y"[].⌂"£n=1`  push a function:
 ♂l                   map length over input
   ╔l                 uniquify
     ;Y               1 if list is empty else 0
       "[].⌂"£n       call this function that many times:
        [].             print an empty list
           ⌂            exit
               =1     1 if length of unique list equals 1 else 0

If the function-only requirement is lifted, the equivalent program works for 15 bytes:

♂l╔l;Y`[].⌂`n=1

Try it online!