Pefectly normal for mal adjusted rear shoes!
The rear brakes are a combination of hydraulic and mechanical.
So if there's a fault with say the h/brake self adjusters there's going to be considerable play as the shoes have worn.
pulling on the brake seperates the shoes into contact with the drim insides which in turn leaves the pistons of the slave cylinder room to expand,
which is why the pedal dips,
the cylinder is expanding to take out the slack until it re contacts the shoes.
An inspection of the drum hand brake mechanisim and shoe wear ought to confirm.
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