Try a can of WD40. This thing is great for squeaky hinges and you can spray it so you don't have to be precise. If it's really far take a stick and strap one to the side of the can with tape and use a piece of thread or tape to make a loop around the top that you can pull to start spraying.
Im not sure i would be able to push down the lid of a WD40 can to make it start spraying.
So far my best idea is this...
I'm going to attach about 30 straws together using electrical tape, then im going to tape the straws to a broom handle to keep the whole thing steady but leaving 1 straw length out either side. Then im going to dip 1 straw end in oil and hold the other end. Then aim it towards squeaky sign hinge and blow or let go.
If i try it with just a cup of oil i'll probably cover the sign, its a shop sign i dont wanna get oil all over it.
Film it, putting the attempt on YouTube. After several million views, you'll make bank. Ask your viewers and subscribers to submit their suggest as to how oil the shop sign given the parameters. Each week, pick one of the suggestions and follow through, filming and uploading the best attempt as well.
End results: How I made millions of dollars off a squeaky shop sign outside my window.
Prior to the day the shop owner decides to change the sign, have millions of followers petition him to not do it.
If he follows through, sue his ass for lost of income. Meanwhile, request suggestions from your YouTube subscribers how to QUICKLY make the new signage squeak, filming those attempts as well.
You'll forever be known as the Squeaky Sign Guy around the world. Then, you'll be off to faraway lands, away from the original squeaky sign helping others, for a fee, of course, to rid the noise of a squeaky sign having similar parameters as once your own that keeps them awake at night.
Bottom line, what others in this thread see as a dude with a squeaky sign problem, I see a potential millionaire. Your call!