What causes tire sealant to seal?
Here's a photo of sealant failing inside a tyre.  These are the latex molecules lumping up together rather than staying in suspension in the carrier liquid which is glycol-based but varies by brand.

These have the glorious name of "boogers" and are a sign the sealant is not going to work very well.  This tyre should be cleaned out completely and a new serve of sealant added.



This is what should happen at the hole when a tyre punctures.  

The carrier is either a water-based glycol/propylene with cellulose and thickener agents like aramid/ceramic fibres, or non-water based latex mix which doesn't need extra thickeners but does have a limited effective life.  Latex also has some level of Ammonia which can contribute to corrosion.
Either product will distribute around the inside of the tyre while you ride.  This leaves a thin layer waiting just inside the area where the puncture forms.

The lighter-weight carrier fluids exit the hole along with the escaping air.  This leaves a visible wet spot on the outside.



As the carrier flows through the hole with the air, the heavier/larger suspended particles get stuck and form a blockage, which slows the air leakage and eventually seals.   In theory, the plug will flex and more air will leak, but the sealant will do the same, continuously packing into the weak spots and stopping the leak.

This only works if the sealant is liquid.  The carrier is volatile and will bleed out through your tyre over time anyway, leaving a dried mess in the tyre.  If your bike is not ridden much, the sealant will pool at the bottom and that's not a lot of use plus it will unbalance the tyre.

Many sealants can be re-energised by adding more fresh product, but mixing brands is an unknown because the chemistry will vary between brands.  Best to dismount the tyre and do a complete clean before changing brands.  Some riders recommend changing tyres every 12 months regardless of wear.