I have a year ago already bought such a cable on Amazon to (then) new Sony Blu-ray players to connect to my my Sony Bravia TV (2008).
The new cable I use to connect HDMI Switcher for TV, because this has only two HDMI inputs, which were both occupied (at the other terminal, the home theater system, which has only a DVD player). The Fire TV Stick and the BRP I now am Switcher (see link below), which goes through the new cable to the TV.
The BRP continues on (as usual) on "auto sensing" (= automatic signal-forwarding or switchover also) to a TV, the TV Stick I have to manually do so far (the Remote Switcher for port selection (terminal) and the menus TV to select the correct TV HDMI input - a bit awkward).
This is the Switcher (it also exists in a 3-port version); Although it acts despite metal housing (at least the frame) is not too high, but fulfilled his services (and has a manual in German language):