Short answer: no. Gigwell sends no automated follow-up or chaser emails, and it has no out-of-office auto-responder. If a buyer mentions receiving a follow-up, it was sent manually by someone on your team rather than generated by the platform.
What you can control is which notifications go out and what someone sees after they submit your booking form.
Change your notification settings
Go to Settings → Documents & Templates → Preferences → Notifications.
Review which notifications are switched on and turn off the ones you don't want going out.
Edit the confirmation message shown after someone submits your booking form. This is the closest thing to an away message — you can use it to set expectations about response times, or to point people somewhere else while you're away.
Save.
Good to know
The confirmation message is shown on screen to whoever submitted the form. It isn't sent as an email reply, so it won't reach someone who emails you directly.
A calendar Hold or a custom status shows nothing at all to someone submitting your booking form. They won't see that a date is tentatively held, and inquiries for that date still come through as normal. If you want people to know a date is unavailable, say so in the confirmation message.
Turning a notification off applies to your organisation's outbound notifications, so check with your team before switching something off that others rely on.
If you want to chase an unsigned contract or an unpaid invoice, you'll need to send the reminder yourself from the booking. There's nothing to schedule, so it's worth building the check into your own weekly routine.