Interesting suggestion. Let's take a look.
We downloaded tweets going back to July 2015 containing the hashtag #IStandWithIsrael. There are several spikes, including two in mid-2016. Let's focus on those. 
Restricting the time range to tweets between 5/1 and 9/1/2016 leaves 25404 unique tweets (73373 including retweets) from 989 accounts. Of the 20 that received the largest number of RTs, 14 have #PJNET in their profiles.
This diagram shows the retweet/reply relationships for #IStandWithIsrael tweets between 5/1 and 9/1/2016. 57 of 989 (5.8%) accounts have #PJNET in their bio, but these accounts earned 25394 or 47969 (53%) total RTs. #PJNET accounts are colored red.
Here's an earlier thread discussing #PJNET and pro-Roy Moore accounts. Among the important points is that PJNET provides tools for partially automating one's account.
The tweet schedules of several of the prominent mid-2016 #IStandWithIsrael users indeed show distinct signs of automation.
Looking at all the distinct #IStandWithIsrael tweets from mid-2016, an overall pattern emerges. The majority of the traffic seems to consist of short, coordinated campaigns.
For the sake of comparison, here's the tweet schedule for #IStandWithIsrael for the last month. Far more organic/disorganized (and volume is lower).
Another thing to check for when looking for automation is accounts that operate 24/7. 70 of the 989 accounts were flagged as such. This set is mostly distinct from the #PJNET accounts - only 6 are in both.
Did the users pushing this trend in mid-2016 have any contact with known Kremlin troll accounts? The short answer is yes (chart is based on replies to/mentions of ten banned IRA accounts).
The #PJNET/#IStandWIthIsrael users had significant interactions over time with five of the banned troll accounts: Jenn_Abrams, tpartynews, TheFoundingSon, TEN_GOP, and Pamela_Moore13.
