The incident was reported on Monday night.
A young male was said to be involved and is described as being about 15 or 16 years old, tall, with dark curly unkempt hair and wearing a grey-coloured sweatshirt.
He was accompanied by a female, described as short, with stocky build and red-coloured hair.
No damage is believed to have been caused to the lights.
Sgt Steven Wilson at Annan Police Station said: “There are strict guidelines for the use of air weapons, and we encourage people to use them responsibly and keep in mind the requirement to have a licence — although that’s not coming in until the end of the year.”
He added: “If people do have old air weapons, air pistols, rifles, anything like that, then just because the amnesty has finished does not mean to say that you cannot surrender air pistols in to any police station or call us to come and pick them up.
“The same conditions will apply — nobody’s going to be in trouble because they hand it in after the amnesty.”