Tripundra or "three horizontals lines" is the Tilak worn by Lord Shiva and His devotees. Urdhva Pundra is tilak worn by Lord Vishnu and His devotees.
But there are images of Brahma with both tilaks.
There are many ambiguous images or representations of Lord Brahma.
The best iconography of Brahma is found in the Puranas (such as Matsya Purāṇa Chapter 260 and Agni Purāṇa chapter 49) and other iconography in some medieval texts on architecture (the most famous being Aparājitapṛcchā Chapter 214, Devatāmūrtiprakaraṇam Chapter 4, Mayamatam Chapter 36) but the tilaka of Lord Brahma was nowhere to be found except in only one book called the Mānasāra
Chapter 51 of the Mānasāra says:
रत्नाङ्गुलीयकौ हस्तौ पादं जालसरत्नकम् ललाटे वृत्ततिलकं स्याच्चन्दनागरुमेव च॥२०॥
His thumb rings and hands should have gems and so should his feet. On his forehead a circular tilaka of sandal (Chandan) and agar paste.
As per the above we can see that a Brahmaji must have a circular tilaka made of sandal and agar, akin to Shakta worshippers (give credit to a good knowledgeable friend for this statement) but the material and maybe the size, being the differentiating factor. This corresponds to the iconography of some of the ancient temples of Southern India as well as roughly the famous Brahma Temple at Pushkar. See the below pictures for the corresponding iconography.
Same Brahma idol with turmeric:
Note: At Pushkar, while decorating the Lord, the idol is given a tripundra or occasionally an Urdhva Pundra too. However as one can see the original idol (without alankara) during abhishekam in the image has a circular tilaka.
From Tamil Nadu:
From Gujarat:
From Aihole, Karnataka:
I am not sure how satisfactory it will answer the question. (I lack the knowledge about any discriptions within puranas or vedas , thus the answer is purely from the perspective of tantra) From Sarvollāsatantram, Sixteenth Ulhassa:
राधातन्त्रे-- जैव: शाक्तो गाणपत्यो वैष्णव: परमेश्वरि । पुष्पेण तिछक॑ भाले सदेव रूपबान भवेत् ॥ प्रत्यक्षैस्तिलकैदेवि शिव सायुज्यमेव च । अनुकल्पैश्व तिलकै: सारूप्यमेति सुन्दरि ॥
O devi, By applying Tilak with the help of flower Shaivas, Shakta, Ganapatya and Vashinav look beautiful as the Gods. Literary by Applying the Tilak one apprently strats becoming like shiva. Applying it with 'Anukalp' gives one a look like shiva himself.
Applying a tilak gives the person, a god like appearance. Thus One can deduce that Gods also apply tilak.
However, there is no mention of Brahma anywhere. There is no sect as large or as equivalent to Shaiva or Vishanva which worship Brahma. Thus it seems the devotees of vishnu used a Urdhva Pundra on Brahma's forehead to make him look like Vishnu and same way devotees of Shiva used the Tripundra to make Bhramha as if Shiva. (Note: These are my conclusions)
Additionally Radhatantram mentions:
त्रिपुण्डं धारयेत् शैव: शाक्तश्न वर्तुलं शिवे । ऊर्ध्वपुण्डूं गाणपत्य: साधकस्यापि लक्षणम् ॥
The Tilak 'Lakshanm': Tripundra by Shaiva , Vartula by Shakta, Urdhva Pundra by Ganapatya.
अथ तिलकप्रमाणमू- वाम रेखात्मिका ब्रह्मा दक्षेेखा सदाशिवः । मध्यस्थाने बसेद् विष्णु: तत्स्थानं नैब लेपयेतू ॥
The Tilak consists of Two lines, the left represents Brahma, the right Sadashiva. In between the two stays Vishnu thus never apply here (never coat with material or "Dravya").
According to Sri Shiva Maha Purana (Section 2.1 - Rudra-saṃhitā (1): Sṛṣṭi-khaṇḍa: Chapter 7 - The dispute between Brahmā and Viṣṇu.)
Brahmā said:—
When lord Nārāyaṇa continued to sleep, an excellent lotus of huge size came out of his navel as desired by Śiva.
It was many Yojanas wide and high. It had an endless stalk. The pericarp was of a brilliant hue.
It was very beautiful with the brilliance of ten million suns. It was wonderful, excellent and worthy of vision containing Tattvas.
Exerting himself as before, Śiva, the great lord, with Pārvatī as his better half created me from His right limb.
O sage, having deluded me with His illusion immediately, Śiva in the course of His sport, produced me through the umbilical lotus of Viṣṇu.
Thus it was that I came to be known as Lotus-born and conceived in a golden womb. I had four faces, red complexion and Tripuṇḍra-marked forehead.
Tripuṇḍra (त्रिपुण्ड्र) or Tripuṇḍraka refers to the “three parallel lines of ash marks over the forehead”, according to the Śivapurāṇa 1.18.
Accordingly, “[...] the Tripuṇḍraka (the three parallel lines of ash marks over the forehead) is the essence of Trinity: Brahmā, Viṣṇu and Rudra. Similarly Maheśvara has retained the esence of everything in the form of Tilaka (the small circular mark) on the forehead. [...]
I hope this clarifies your queries.
