OK I finally managed to get the two connectors apart, so just in case anyone in the future has the same trouble as I did, here's the details:
The larger rectangular connector is held together by a single clip, which is released by squeezing the connector on the main loom side. There's a tab on the connector on the fairing side, but this doesn't actually seem to do anything. This connector was just a bit stiff, and also some of the terminals were starting to corrode, as mentioned in the above post by tommyardin.
The smaller connector is the really confusing one. The connector on the fairing side is actually in three pieces. There's the outer shell and then an inner section which holds in place a rubber seal. The clips visible on the outside of this connector (one on each short edge) are just there to hold the three pieces together and don't need to be unclipped to separate the two halves of the connector. The clip which holds the two halves of the connector together is next to the middle red and black wire on the main loom side, and the tab needs to be pulled outwards in order to release. I found a picture of the connector type, which is probably a bit clearer than my explanation.
The larger rectangular connector is held together by a single clip, which is released by squeezing the connector on the main loom side. There's a tab on the connector on the fairing side, but this doesn't actually seem to do anything. This connector was just a bit stiff, and also some of the terminals were starting to corrode, as mentioned in the above post by tommyardin.
The smaller connector is the really confusing one. The connector on the fairing side is actually in three pieces. There's the outer shell and then an inner section which holds in place a rubber seal. The clips visible on the outside of this connector (one on each short edge) are just there to hold the three pieces together and don't need to be unclipped to separate the two halves of the connector. The clip which holds the two halves of the connector together is next to the middle red and black wire on the main loom side, and the tab needs to be pulled outwards in order to release. I found a picture of the connector type, which is probably a bit clearer than my explanation.