We can only speculate. Dasrath Sharma rather puts Bhinmal (Gurjara) as the birth place of Parihars; however based on demography of Parihar Rajputs - Central India specially Ujjain Gwalior region seems a more likely origin since this tract has been dominated by Parihars till this day - having 2 princely states till end. All these are speculations . When we talk of Parihars , there are three broad sections: Mandore Parihars - Inda, Dewal, Bela ; Imperial/Malwa Parihars - Kalhans, Narauni etc and Gurjara Parihars - Bargujar & subclans like Madhadh, Sikarwar.
This is how the khaap /sub-lineages exist today. It is Unfortunate that Imperial Pratihars are conflated with Gurjara Pratihars; the latter was only subgroup of the former.
Yes, we are aware of Somwanshi subclan Palwar who take Pali as origin. They are found in Faizabad, Gorakhpur & Azamgarh region Palwar Rajputs of Purvanchal