Can you suggest any methods or services for finding the domain owner's contact information if it's not available on WHOIS? Also, what are some ways to bypass privacy protection in WHOIS?

No way, because that would defeat the purpose of having a private status. However, you could attempt to request being removed from the registrar by explaining the situation.

There are also some services that display the record of modifications made to the whois information of domains. Occasionally, you may stumble upon contact details there that haven't been obtained yet.

Most registrars offer contact options through their website. For instance, if you look at .com domains, their address is privacyprotect.org and there's a "Contact Domain Owner" form available immediately. Meanwhile, for .fr domains, the address is client.naunet.fr/c/whoiscontact.

Attempt to penetrate other areas of the host (if present). Check if there are any additional websites on the same server, which may also be owned by the same person.

Utilize resources like 2ip.ru, as there are several comparable services available. If any additional domains are found, use domain history tools like www.domaintools.com/research/whois-history/ to further investigate.

I've been on my mobile for an hour, and in around 10 minutes, I will be in the city.

One effective approach is to utilize specialized services like DomainTools or WHOISXML API, which can sometimes provide historical WHOIS records or additional insights.
Another option is to check the website itself for contact details, often found in the footer or 'About' section. If the domain has a social media presence, reaching out through those channels can yield results.