In KOH solution your product is the potassium carboxylate salt, which you will struggle to mobilise on silica gel.
You could do a mini workup: partition a drop or two of you reaction mixture between 0.1 mL dilute HCl and 0.1 mL ethyl acetate, then TLC the ethyl acetate layer and you should see the carboxylic acid product.
However, if a direct TLC of your reaction mixture shows no starting material, then you have complete conversion and can quench the reaction. This is normally how I judge the endpoint of saponification reactions.
Placing the TLC plate under high vacuum to get rid of most of the water is a generally a good idea when analysing aqueous solutions, but leave it too long and in this case you risk evaporating any remaining DEM (i.e. the conversion may appear higher than it really is).