The traditional Scotchlok 560 as on the OP's ceiling and its different size variants, are an older, basic design of insulation displacement connector that IMO has been superseded by newer, better technologies. But they were very popular in their heyday when there wasn't much else to match them and retain their place in the market. Many people cite reliability concerns but there might be something of a self-fulfilling prophecy: They are relegated to rough-and-ready applications such as exterior vehicle wiring, are poorly installed by inexpert users with incorrect cable sizes and exposure to salt spray and cable movement, where even a more substantial connector might also suffer reduced reliability.
As some have mentioned, we have never used them in premises wiring in the UK. In the US I believe they are more commonly found in manufactured products, but are accepted for some applications in premises wiring. I find them for example in AC power wiring within US-made large exterior displays. There have been times when I have found a bunch of Scotchloks and been annoyed that they all worked fine, despite vibration, moisture etc, and hence failed to support my argument that they were an inadequate type of connector.
Important factors to note are that they must not be used with aluminum wire, only copper strictly in their approved gauge range (which is sometimes different between the tap and the through cable.) Importantly, their permitted current flowing across to the tap connection may be lower than that of the wire itself. This is a sneaky limitation that one should always check for with any connector, as once it is installed, future alterations may fail to locate any under-specced connectors that have been used and overload the connectors even while correctly observing the ampacity of the wiring.
