Chapter 1 of the Koṭirudra Saṃhitā of the Shiva Purana places the Linga in a cremation ground or citābhūmi (and alternatively at a place called parali):
वैद्यनाथं चिताभूमौ - Vaidyanātha in the cremation ground
The Dvādaśaliṅgastōtram by Adi Shankaracharya places the Linga in the North Eastern part of the country:
पूर्वोत्तरे प्रज्वलिकानिधाने सदावसन्तं गिरिजासमेतम्।
सुरासुराराधितपादपद्मं श्रीवैद्यनाथं तमहं नमामि॥५॥
I bow to that Lord Vaidyanatha who always lives in the North East in the cremation ground with the Daughter of the mountain and whose lotus feet are worshipped by the devatas and the asuras
This indicates that the Linga is situated in the North east alongwith Devi Parvati, an indication to a śaktipīṭha in the vicinity, just like Mallikarjuna.
In the Devi Bhagavata Purana’s list of 108 śaktipīṭhas (7.30), and Devi Gita part of Devi Bhagavata Purana (7.38) there’s a mention of one At Vaidyanatha:
as Ārogyā in Vaidyānātha
- Skandha 7 Chapter 30
The excellent place of Bagalā in Baidyanāth
- Skandha 7 Chapter 38 (Devi Gita)
Accordingly based on the above, we can conclude that the Vaidyanātha Jyōtirliṅga is located in the North eastern part of the country near a śaktipīṭha,
The Vaidyanaatha of Deoghar Jharkhand, has a śaktipīṭha facing the Jyotirlinga temple and the place is claimed to be known as chitabhumi in common parlance. There are only 4 śaktipīṭhas in modern day Maharashtra and Parli doesn’t feature in that list.
Deoghar Jharkhand being roughly in the north eastern part of the country and also near a famous śaktipīṭha is the correct Vaidyanātha Jyōtirliṅga.
The Jyotirlinga temple and Shakti pitha at Deoghar Jharkhand, connected to each other by red threads.
Note: There’s an alternate version of the Dvādaśaliṅgastōtram where cremation ground is replaced with parali and sadavasantam is replaced with sadashivam. Yet the basic north east and alongwith Devi Parvati is retained. No doubt Parli has its significance, yet it is not the jyotirlinga spoken off in scriptures.