Does the forearm grip/handshake have a historical basis?

It's not European. It's African & Middle Eastern. Prior to modern day plumbing. It was offensive to shake with the right hand. The right hand was/is used to clean ones self after secretion, so LEFT forearm shakes were done to avoid touching ones hand that was used to wipe themselves. Their a culture that respects hygiene. Not like here in the States. Certain men & women are known to never wash their hands after urinating & defecating. NASTY!

I have been taught that this form of handshake was brought about during the time of Vikings warriors would grab the forearm to prove and to feel for hidden daggers in case of assassination attempts...

Here are two (not very good) references that attribute the forearm handshake to the Romans, if not earlier, along with other interesting background regarding the forearm handshake and similar variations on the common modern handshake:

• An Analysis of Handshake Styles

Shaking hands is a relic of our ancient past. Whenever primitive tribes met under friendly conditions, they would hold their arms out with their palms exposed to show that no weapons were being held or concealed. In Roman times, the practice of carrying a concealed dagger in the sleeve was common so for protection the Romans developed the Lower-Arm-Grasp as a common greeting.

Lower-Arm-Grasp

• LAKOTA COUNTRY TIMES - "Your handshake can say a lot", by Jim Kent

I can recall being given instructions on “a proper handshake” by my uncle as a skinny little kid growing up in Brooklyn. I was told that the custom dated back to Roman times - when men grasped not only one’s hand, but the entire forearm to ensure that the person you were greeting had no hidden weapons. My interest in history, even at that young age, re-enforced my understanding that this social expression was something to be taken seriously. I pass on the instructions I received any time a child or adolescent offers me a half-hearted handshake. My wife is even more dedicated than I about such social education. Over the years, I’ve heard the “hand-shake origin story” shift to medieval times as well as ancient Egypt. Whatever the truth behind the tale, the fact remains that the ritual has been around, more or less, forever. There have been variations on it -from the “soul brother” clasp that began in the 60s, to the similar “brothers in arms” grasp first used by many Vietnam vets, to the countless adaptations created by diverse social groups

Unfortunately, these references don't bring reliable sources for their contentions, although I personally can attest to witnessing in NYC the variations cited by Jim Kent in the '60's and the Vietnam War era, and noting that they were new for that period. I always understood that such gestures are related to the gesture of reassuring or encouraging someone to be strong and stalwart by firmly grasping their arm or shoulder. The two parties exchange such a gesture, encouraging each other to be strong and united. This makes sense, given that this sort of greeting was particular to groups that considered themselves "comrades in arms", etc., and so perhaps this sort of thing hearkens back to some ancient form of warrior greeting. Admittedly though, this amounts to nothing more than interesting speculation.

I suppose I can lay claim to being a "primary source" on such a thing, and IMO, when we encounter such forms of greeting today, they date back to those 1960's forms, just as do many other contemporary customs and fashions.

The history section of the wikipedia article on handshakes suggests that the Greeks were familiar with the custom at least since the 5th century BC (because we have a sculpture showing Hera and Athena shaking hands that has been dated to the 5th century BC).

Source

Romans also used handshake. It was depicted on Roman coins to symbolize agreement and compromise.

The earliest reference I can find comes from a 1937 commentary on Shakespeare's "Julius Caesar", although there are many later references that this handshake was taught to the actors by Lawrence Alma-Tadema in a 1898 staging of the play. It seems to have been often used in this play since, and I could find an example from a 2005 staging.

Almost all references to it is from 2010 and later, which probably is because "cool" teenagers seldom go to watch Shakespeare in a theatre. So this handshake didn't become a "thing" until it popped up in TV and Movies. It seems it is the TV-series "Spartacus" we have to blame/thank for this.

However, there are no Roman era depictions of this handshake that I can find, and there are plenty of depictions of ordinary handshakes from the Roman era, so we have to conclude that it's attribution as a roman handshake is a later invention. That probably goes for the handshake itself as well, although that's less certain.

It's probably invented in the theatre to make the handshake look dramatic, and the prime suspect is Alma-Tadema himself, although this is pure conjecture.