><>, 32 30 bytes

• Had a redundant !o.

"@!qx:q:"ooi~i~i~i{=?;o!o!ox~oo;

Explanation

><>, 32 30 29 bytes

• Had a redundant !o.
• -1 byte thanks to Aaron.

iii0["@!qx:q:"ooi{=?;o!ox~oo;

Explanation (old)

(will update soon)

"@!qx:q:"ooi~i~i~i{=?;o!ox~oo;
"@!qx:q:"                        Push @!qx:q: on the stack (in reverse)
         oo                      Print :q [stack: @!qx:]
           i~i~i~                Remove first 3 input characters
                 i               Load @ or : from the input (= i)
                  {              Shift stack to the left [stack: !qx:i@]
                   =?            If 4th character was @
                     ;              Exit
                                 Else
                      o             Print :
                       !o         Jump to
                         x        Random direction (left or right because
                                  up and down retrigger x)
                                     Left:
                     ;o!o               Print x and exit.
                                     Right:
                          ~oo;          Remove x, print q! and exit.

"@!qx:q:"ooi~i~i~i{=?;o!ox~oo;
"@!qx:q:"                        Push @!qx:q: on the stack (in reverse)
         oo                      Print :q [stack: @!qx:]
           i~i~i~                Remove first 3 input characters
                 i               Load @ or : from the input (= i)
                  {              Shift stack to the left [stack: !qx:i@]
                   =?            If 4th character was @
                     ;              Exit
                                 Else
                      o             Print :
                       !o           Jump to
                         x          Random direction (left or right because
                                    up and down retrigger x)
                                       Left:
                     ;o!o                 Print x and exit.
                                       Right:
                          ~oo;            Remove x, print q! and exit.

><>, 32 bytes

"@!qx:q:"ooi~i~i~i{=?;o!o!ox~oo;

Try it online!

><>, 32 30 bytes

• Had a redundant !o.

"@!qx:q:"ooi~i~i~i{=?;o!o!ox~oo;

Try it online!

Explanation

"@!qx:q:"ooi~i~i~i{=?;o!ox~oo;
"@!qx:q:"                        Push @!qx:q: on the stack (in reverse)
         oo                      Print :q [stack: @!qx:]
           i~i~i~                Remove first 3 input characters
                 i               Load @ or : from the input (= i)
                  {              Shift stack to the left [stack: !qx:i@]
                   =?            If 4th character was @
                     ;              Exit
                                 Else
                      o             Print :
                       !o         Jump to
                         x        Random direction (left or right because
                                  up and down retrigger x)
                                     Left:
                     ;o!o               Print x and exit.
                                     Right:
                          ~oo;          Remove x, print q! and exit.