When the option actually appears
The redirect option only exists once DPD has scanned the parcel into their network. A retailer's dispatch email arrives well before that, sometimes a full day before, and during that window DPD's tracking page just says they're expecting it. Nothing you press will redirect a parcel DPD hasn't got yet.
Once it's scanned in, the option is usually open until the parcel is loaded for delivery. On a normal week that's an evening. On a busy drop week, when the depot turns parcels around overnight, it can be a couple of hours.
Why resellers miss it
Because the window opens at an unpredictable time and closes fast. If you've got eight parcels landing from three retailers, you'd need to be checking eight tracking pages through the evening to catch each one at the right moment. Most people check once, see "not available yet", and forget until the driver's already been.
The other trap is the postcode. DPD verifies the recipient with the delivery postcode, and a typo or an old postcode locks you out of the redirect for that parcel after a few attempts.
What a good setup looks like
Pick the shop once. Every parcel to that address goes to the same shop, so the choice should be saved, not made per parcel.
Let something watch for you. The moment DPD receives the parcel, the redirect gets booked and you get the confirmation and collection code by email. You never open a tracking page.
Have a second and third choice. Parcel Shops go full or close early. If the first one can't take it, the booking should fall through to the next one on your list without you being involved.
That's what Minted's parcel tracking does for members: it picks up dispatch emails from your inbox, watches each DPD parcel, and books the redirect to your saved shop as soon as it can. Redirected parcels stay on your tracker marked as such, with the collection details attached.