Pashupat Vrata is intended for the release of bondage and thus liberation. The Srutis like Atharvasiras Upanishad state in single line about how to perform Pasupat Vrata which I also discuss here:
अग्निरिति भस्म वायुरिति भस्म जलमिति भस्म स्थलमिति भस्म व्योमेति भस्म सर्वंह वा इदं भस्म मन एतानि
चक्षूंषि यस्माद्व्रतमिदं पाशुपतं यद्भस्म नाङ्गानि
संस्पृशेत्तस्माद्ब्रह्म तदेतत्पाशुपतं पशुपाश
विमोक्षणाय ॥ ५॥
He converts fire, air, water, earth, ether and everything that exists here in to ash. He who sees this and mentally realizes it and observes the “penance to Pashupati ” and who coats ash all over his body with this ash attains the state of Brahman. By worshipping “Pasupathi” like this, the ties of bondage of all beings get cut and they attain salvation.
But it is very short and ritualistic methods aren't also given. Also in Ishwara Gita of Kurma Purana Lord Maheswara states:
मदात्मा मन्मना भस्म गृहीत्वा त्वग्निहोत्रिकम् ।
चिन्तयेत्स्वात्मनीशानं परं ज्योतिः स्वरुपिणम् ।
एष पाशुपतो योगः पशुपाशविमुक्तये ।।
सर्ववेदान्तमार्गोऽयमत्याश्रममिति श्रुतिः ।
एतत्परतरं गुह्यं मत्सायुज्यप्रदायकम् ।।
One should meditate upon me and turning to my Bhasma form, should accept the ashes of Yajna. These ashes should be applied over all limbs of the body sanctified with the hymns of Agni etc.. and Aditya. Thereafter one should invoke in his soul the respledant Ishana. This is the Pashupata Yoga for the recluse of the Jiva from the bondage and is as per Vedanta marga. This is beneficial in all the asramas, as has been ordained by the Srutis. This is better than the best and is extremely secret, and bestows my Sayujya.
So, it is likely that the procedure to perform it is described in some Vedas/Vedic sources as Lord Maheswara says 'has been ordained by Srutis' and Lord Shiva also tells it bestows his Sayujya, Where is this mentioned in Vedas? How to perform Pashupat Vrata as per Vedas?