Will I be asked for an onward ticket upon my second 60-day visa exemption arrival in Thailand?

You can ALWAYS be asked for proof of onward travel when entering visa exempt. It's a requirement for that entry type. Whether it's your first entry or your 10th.

It's not common to be asked by immigration, unless they are looking for a reason to cause trouble for you.

2nd entry in 12 months isn't much information. That could mean your last entry was a year ago, or 3 months ago. Those are not the same for your chances.

It's much more common for your airline to require this as part of your check-in though.