Hi folks,
First time posting here. I have a 2002 Sequoia that I purchased used last fall. I have this weird buzzing sound coming from inside one of the fuseboxes under the hood. It's coming from a purple relay that is labeled "starter relay" on the side. It only seems to start buzzing right around freezing temps.

Last fall it was doing it, and I noticed the daytime running lamps were staying on, too. I disconnected them via the connector next to the battery and thought the problem went away, but it started again last night as we found out when the vehicle's alarm went off at 1am.

If I disconnect the battery for a few minutes, then reconnect it, the buzzing stops for a little while, then starts up again. Slow buzzing at first, then fast.

Any ideas or suggestions are most appreciated.