Hey Wayne! 
I’ve been waiting to reply to you because I was testing out the two Pixel phones I got. Overall the experience was great. The eBay sellers were good, and the phones are awesome. Lightweight device, fast to tap around on to get things done, and GrapheneOS is so delightfully clean and of course, most importantly de-googled. 
The one issue I had was that both phones had delayed notification issues for SMS text messages. Sometimes I would get notified of new texts right away, but most of the time I would only see them when I unlocked the phone. After searching online I found lots of other people with Pixel 2, 3, and 4 phones who experience this as well. According to GrapheneOS it’s an issue in the AOSP (Android Open Source Project) firmware.
There is a solution however! 
I installed an app called Signal and set it to be the default SMS app in Settings. That worked perfectly, I was notified of every text immediately after that–which does seem to confirm that it’s a firmware issue.
Btw, I installed Signal via APK from their site so I didn’t have to use an app store, but I’m sure finding and downloading another app via F-droid or Aurora that sends and receives SMS would work wonderfully as well. 
So, even though that worked awesomely, I actually decided to go a totally different direction regarding de-googled phones for me and my family. My plan is to wait till mid-January for these /e/ phones, so I’m selling both the Pixels on forum, here: Classifieds - Jeff.pro.
Also, I came across two links during the the last few weeks that I found helpful/interesting and I thought you might too. This is a post here on the forums that you may have already seen: Graphene OS - DIY De-Googled phone explained!. And this is a site where I heard some JP admins are de-googling phones to sell: https://azadius.com.
Hope all this helps! Let us know how your journey goes 