Regarding applying Tilaka from water

[Yasoda Jivan dasa]

Namaskāraḥ respected vidvaj-janas,

I humbly seek clarification regarding the śāstric basis for applying ūrdhva-puṇḍra or any form of tilaka using only water. Specifically, is there any authoritative scriptural reference—whether from Vedic, Purāṇic, Smṛti, or Vaiṣṇava texts—that permits the application of tilaka solely with water as a valid substitute in the absence of traditional materials such as candana, gopī-candana, bhasma, or similar substances?

I would be grateful for exact citations and contextual explanations from authentic sources.