The design is the visual features of the portion of the ELECTRIC DEVICE MOUNTING BRACKET shown with solid lines in the drawings, whether those features are features of one of shape, configuration, ornament or pattern or are a combination of any of these features.Drawings of the design are included, as follows:FIG. 1 is a perspective view of an ELECTRIC DEVICE MOUNTING BRACKET showing the design in a retracted position;FIG. 2 is a front elevation view of the design of Figure 1;FIG. 3 is a left side elevation view of the design of Figure 1, wherein the right side elevation view is a mirror image thereof;FIG. 4 is a plan view of the design of Figure 1, wherein the bottom view is a mirror image thereof;FIG. 5 is a rear view of the design of Figure 1;FIG. 6 is a perspective view of an ELECTRIC DEVICE MOUNTING BRACKET showing the design in an extended position;FIG. 7 is a front elevation view of the design of Figure 6;FIG. 8 is a left side elevation view of the design of Figure 6, wherein the right side elevation view is a mirror image thereof;FIG. 9 is a plan view of the design of Figure 6, wherein the bottom view is a mirror image thereof;FIG. 10 is a rear view of the design of Figure 6;FIG. 11 is a perspective view of an ELECTRIC DEVICE MOUNTING BRACKET showing a first variant of the design in a retracted position;FIG. 12 is a front elevation view of the variant of Figure 11;FIG. 13 is a left side elevation view of the variant of Figure 11, wherein the right side elevation view is a mirror image thereof;FIG. 14 is a plan view of the variant of Figure 11, wherein the bottom view is a mirror image thereof;FIG. 15 is a rear view of the design of Figure 11;FIG. 16 is a perspective view of an ELETRIC DEVICE MOUNTING BRACKET showing the first variant in an extended position;FIG. 17 is a front elevation view of the design of Figure 16;FIG. 18 is a left side elevation view of the variant of Figure 16, wherein the right side elevation view is a mirror image thereof;FIG. 19 is a plan view of the variant of Figure 16, wherein the bottom view is a mirror image thereof;FIG. 20 is a rear view of the variant of Figure 16;FIG. 21 is a perspective view of an ELECTRIC DEVICE MOUNTING BRACKET showing a second variant of the design in a retracted position;FIG. 22 is a front elevation view of the variant of Figure 21;FIG. 23 is a left side elevation view of the variant of Figure 21, wherein the right side elevation view is a mirror image thereof;FIG. 24 is a plan view of the variant of Figure 21; wherein the bottom view is a mirror image thereof;FIG. 25 is a rear view of the design of Figure 21;FIG. 26 is a perspective view of an ELECTRIC DEVICE MOUNTING BRACKET showing the second variant in an extended position;FIG. 27 is a front elevation view of the design of Figure 26;FIG. 28 is a left side elevation view of the variant of Figure 26, wherein the right side elevation view is a mirror image thereof;FIG. 29 is a plan view of the variant of Figure 26, wherein the bottom view is a mirror image thereof;FIG. 30 is a rear view of the variant of Figure 26.