Hello and thank you for coming to Just Answer and allowing us a chance to help you with your question. According to documention on the Federal Aviation Administration's (FAA) website, as late as 1996, airlines and airport security were only requested (a recommendation, not a requirement) to check passenger identification in the event of a condition of high security alert. There were concerns that passengers would object, however, it was expected that the passengers would accept an identification check during a time of high security alerts. Prior to 9/11, air travel security focused on luggage and personnel searches and didn't focus on identifying or banning passengers considered dangerous.
The requirement for passenger identification in order to fly was imposed by the Transportation Security Administration post 9/11 and was considered a necessary part of the overall increased air travel security, since not all of the 9/11 hijackers had valid identification and some of them might have been stopped had they been required to show identification before boarding the aircraft.
I hope this answers your question. I will be happy to provide additional clarification about this answer or links to supporting documentation if you would like.
I've searched the FAA website for any references to Level 4 security prior to 2001 and I've only found one reference. Most of the aviation security procedures were changed due to 9/11 and many of the security procedures were canceled when airline security was handed over to the newly-formed TSA. The references I've seen to the FAA's security procedures suggest that information was classified (security clearance and need-to-know were required to view it) and the government is slow to release formerly classified information. The search keywords that I have found that provide any information are "AVSEC Level IV".
This document on the FAA website is an emergency plan for the Alaskan region as of 1995 but it does list the alert levels and the requirements for the alert levels, but I haven't been able to completely open this document on my computer. I have seen the table of contents, so I think it contains the information that you need, but it keeps partially opening and then hanging on my computer. I hope it will open for you. https://www.faa.gov/search/?omni=MainSearch&q=avsec+level+4&x=40&y=11 is the search page and the document you want is the one identified as "Order".
Sorry I can't provide more help, but the FAA's website is at www.faa.gov and you may be able to find more information than I can.