How To make brown packing tape look aged?

I'm putting together a couple dozen cardboard boxes that need to look like they've been in storage for a couple decades. We're fortunate to actually have a bunch of old boxes that were literally pulled out of storage, this week (yes, this is low budget...), and look worn, but they were flattened out when given to us, with tape removed. So we need to reapply tape.

We have the brown tape that movers typically use (as opposed to clear) and that's what the director wants, but it all looks too shiny and new. Any tips on how to age the tape enough that it matches the boxes? If we go as basic as just applying something to mimic dust, what would you suggest? (These will be for an immersive experience, so they will be seen up close, even handled.)

(This might be really basic, so I apologize for the simple question. I'm just more on the building side of things than props, but I've had to jump in, in a pinch.)