The ornamental design for a side mount actuator with push button, as shown and described.
FIG. 1 is a first perspective view of a side mount actuator with push button showing my design;
FIG. 2 is a second perspective view thereof;
FIG. 3 is a front view thereof;
FIG. 4 is a back view thereof;
FIG. 5 is a left side view thereof;
FIG. 6 is a right side view thereof;
FIG. 7 is a top view thereof; and,
FIG. 8 is a bottom view thereof.
The dashed or broken lines shown in the drawings depict portions of the side mount actuator with push button in which the design is embodied that form no part of the claimed design.