So there's probably a "more clean" way through the data editor, but using triggers you could have a trigger that fires when your Goliath uses a load ability on the Dropship (you'd have to create this "dummy" load ability) which enables movement and changes ownership of the Dropship.
Upon unload you could have a second trigger fire that changes ownership back to neutral and disables movement again.
Alternately if you didn't want to add an ability to the Goliath like that you could have a trigger fire when the Goliath walks within X distance of the Dropship that does the above. That may lead to accidental loadings though.
A third option would be to have the ability on the Dropship and add control to your unit when in range (like a merchant, I think there's a flag to do this, but there are tutorials on here for it as well). This way when you walk in range of the Dropship you gain temporary control of it so that you can click load which will then make you the owner.