Blast From the Past: Study Historical Display not appearing

I have not had any issues with the Blast for the past!  Just saying..... 

I ... do not have..... or ever had... CC or Mod's.  I also do not have any EP's after MWS.  Just pointing out a fact for me.  I play on Microsoft PC not laptop. 

I had the same Problem. No matter what I looked at. Whether it was a picture or a statue. I noticed that the wishes were always in focus. The wish was always to look at a picture, and it always completed the wish. 
I deactivated the wishes and fears in the settings and then traveld to another museum. After thirty minutes of Sim time, it completed the quest for me.
Maybe I can help someone with this tip.
I play on the PS5.

No mods or CC , different museums different objects and still it won't complete. 

I didn't have any issues with just the "View" option. I took my sim to Plumbbob Pictures Museum in Del Sol Valley, clicked View on the giant dinosaur head and just let it complete and the quest task completed. I didn't have to queue up anything else or do anything special.

OMG THANK YOU!!! y'all this works!!! 

You have to let your Sim view the art until they're done. Like my Sim viewed a statue, & then when another Sim showed up, started up a conversation, so the view was completed. That unlocked the next prompt.

I just had to “view” on the item until it auto stopped; I didn’t get the option for “study” 

I'm having the same issue. I removed my mods and deleted the localthumbcache, and repaired the game, and I only get the option to view statues and paintings, but not to study historical display. Clicking view on any valid items in the museum doesn't complete the task. 

It worked! Yaaay thank you 😊 I used the same table and statue at the museum in Brindleton Bay, and clicked 'view'.  My sim was also inspired at the time, not sure if that makes a difference. 

'On the hunt' statue placed on a table worked for me as well. Thanks to the person who suggested this