Send email after interview?

[Shwish]

I interviewed last week for a job I want. Sent a follow up email to thank them for their time a couple of hours afterwards and they replied and asked me to come back a couple of days later for a second. I was quite surprised if I'm honest because id be a bit of a punt. I don't have experience in this area. However I was very honest and they said they didn't mind training the right person.
So I had the second round today. I think it went well. My question is - should I email again? Or will that look too pushy / creepy?
I'm just thinking it seemed to help the first time (or maybe it didn't and was just a coincidence)
If you're hiring someone would you think it was a sign of keenness or desperation if they emailed after both interviews? Thanks

I'd see it as enthusiastic and professional.

I think I would. Probably something along the lines of thanking them for the opportunity to discuss the job further and how much you appreciated their time and input. It doesn’t have to be long and creepy. Just short, sweet and positive. Good luck!

I don’t think there is anything wrong in being keen.

You could thank them for their time, tell them your keen on the role and that you feel
you would be a good fit for the role, perhaps
say something else pertinent.

It depends, was the interview with the same people??

I’ve been an interviewer a thousand times (or many hundreds) and I always look positively on a candidate who follows up on an interview with a quick thank you. I was advised to do it by a family friend who worked for a big investment bank in NYC back when I was in university and I’ve always done it since. It always helps. Do it!

I think it's industry dependent. Anyone who did this who I'd interviewed I would roll my eyes at. It wouldn't stop them progressing if they were a good candidate but it would definitely be seen as a bit try-hard.

But in many places it would be welcomed.

Thanks everyone. I just sent it. The person who's contact details I have interviewed me both times (along with others) so I wasn't really sure if it would be weird to mail for a second time. Decided to just keep it as a thank you and feel free to contact me if you have any further questions type email.
Hopefully she won't be rolling her eyes at me 😆