2007 Accent GS start up noise, water pump?

I've got a 2007 Accent GS with 167k miles in it. When it starts up, it makes a noise from the back passenger side of the engine and I'm thinking it might be the water pump. No other signs or symptoms like overheating and the noise goes away after warmup.

The timing belt has a 60,000 mile service interval and I've owned this car since 153k. I will probably have the timing belt and water pump replaced soon anyway.

I've included 2 videos that have the noise during immediate start up and after it's warmed up. I accidentally titled the videos backwards on YouTube. The links here are right.

Sounds after warm up

Sounds on start