Combined per your notes: the house stays put and gently floats, the window pops in, and the glow now builds to a strong "lights-on" finish.
The H house gently floats up and down the whole time. The green window pops in, and its glow builds up and holds strong - the finished, lit look you liked. No more dropping in from nowhere.
96px (Gmail size)
animated - circle
animated - squareGoogle freezes profile photos, so for the actual Gmail/Google profile picture use this still - it's the finished glowing frame. Use the animated GIF above for your email signature, website, and social profiles, where motion plays.
96px (Gmail size)
static - circle