Hi there - I worked as a food safety manager at a pasteurized egg plant for 20 years, and we told a LOT of pasteurized eggs to a mayo producer. Eggs are considered a high-risk ingredient, because of the definition that someone provided above.
We provided a COA to our customer for every lot. We never shipped eggs until the micro results were available, and the COA (including Salmonella, TPC, coliforms, yeast, mold, and Staph) was provided with the shipment or prior to shipment.
The reason that our customer considered the eggs, even though they are pasteurized, to be high risk, is because of the risk of post process contamination, and the history of foodborne illness associated with egg. With this history, it's difficult to make that case to an auditor that eggs are not high risk.
At my current job, we use eggs at our plant, and we have used the Supplier Control (FSMA) to control the risk. You need a copy of their third-party audit from a GFSI accredited certifying body such as SQF, BRC or similar, which you have reviewed for any food safety red flags. You should also have receiving procedures including a truck inspection/temperature check <40 F with corrective actions if not in spec, that a COA is required prior to use, and temperature monitoring for the cooler you store the eggs in, just like any other refrigerated item. Lastly, you should have instructions for sanitary handling during production to show that you are preventing environmental contamination as you add egg to the mayo. All this should be in your risk analysis. Even though mayo is an acidified product, salmonella has been proven to grow in low pH items such as orange juice. It's not wise to rely on pH only as a CCP without a kill step in your process.
It sounds like a lot but once it's in place it really works well.