Hare Kṛṣṇa,
The best (and may be the only way) to associate with Kṛṣṇa when He is not present is through any (or all) of the nine different kinds of devotional service through feelings of separation. We can learn this from the gopīs of Vṛndāvana.
“The gopīs of Vṛndāvana were so attached to Kṛṣṇa that they were not satisfied simply with the rāsa dance at night. They wanted to associate with Him and enjoy His company during the daytime also. When Kṛṣṇa went to the forest with His cowherd boy friends and cows, the gopīs did not physically take part, but their hearts went with Him. And because their hearts went, they were able to enjoy His company through strong feelings of separation. To acquire this strong feeling of separation is the teaching of Lord Caitanya and His direct disciplic succession of Gosvāmīs. When we are not in physical contact with Kṛṣṇa, we can associate with Him like the gopīs, through feelings of separation. Kṛṣṇa’s transcendental form, qualities, pastimes, and entourage are all identical with Him. There are nine different kinds of devotional service. Devotional service to Kṛṣṇa in feelings of separation elevates the devotee to the highest perfectional level, to the level of the gopīs.” (Texts 1-5: Kṛṣṇa Book)
It is also advised that “those who are in the disciplic succession of the Mādhva-Gauḍīya-sampradāya should also feel the separation of Kṛṣṇa, worship His transcendental form, and discuss His transcendental teachings, His pastimes, His qualities, His entourage and His associations.” (Texts 1-5: Kṛṣṇa Book)
As sadhakas (practitioners of bhakti), we can follow in the footsteps of the gopis. How were they associating with Kṛṣṇa in His absence?
“The gopis spent their nights as previously described, directly associating with Kṛṣṇa by singing and dancing, conversing, kissing and relishing conjugal rasa. In the daytime, they could only associate with Kṛṣṇa by thinking of Him. Drinking the nectar of Kṛṣṇa’s flute song, the gopis became immersed in the rasa of separation. When Kṛṣṇa went to the forest to herd the cows, the gopis’ minds chased after Him.” (SB 10.35.1: Sārārtha-darśini)
As a matter of caution, we cannot imitate exalted devotees such as the gopis. The least we can do is remember Kṛṣṇa by thinking of Him. We can read scriptures that glories His name, form, qualities, pastimes, abode, etc. We can associate with devotees and engage in Krsna-katha (as we are doing in this sadhusangaonline forum). We can sing kirtan for Him. We can preach. We can cook for Him. We can make garlands for Him. We can serve His devotees. Most importantly whatever we do, our mind should be completely absorbed in Krsna consciousness.
Yena tena prakāreṇa manaḥ kṛṣṇe niveśayet [Brs. 1.2.4]. That is the instruction of Rūpa Gosvāmī, “Some way or other, just engage your mind in Kṛṣṇa.”
“Kṛṣṇa can be present more acutely in separation. That is Caitanya Mahāprabhu’s teaching: to love Kṛṣṇa in separation. Just like Caitanya Mahāprabhu in separation: govinda-viraheṇa me. Śūnyāyitaṁ jagat sarvaṁ govinda-viraheṇa me. He was thinking that “Everything is vacant without Govinda, without Kṛṣṇa.” (SP Lecture on SB 1.8.39)
This is a great transcendental art to learn how to love Kṛṣṇa in separation.
Therefore, the key lesson and implication from this pastime is how Kṛṣṇa is teaching us that devotional service to Him in feelings of separation elevates the devotee to the highest perfectional level, to the level of the gopīs. The various purpose of Kṛṣṇa’s unlimited pastimes is to enhance the pleasure of the devotees. Killing the demons or establishing religion are secondary reasons. Kṛṣṇa lives for the devotees and devotees live for Kṛṣṇa. Each is in a transcendental competition to enhance the other side’s love and pleasure.
“Persons who are constantly engaged in the transcendental meditation of seeing Kṛṣṇa, internally and externally, by thinking of Him playing the flute and entering the Vṛndāvana forest, have really attained the perfection of samādhi. Samādhi (trance) means absorption of all the activities of the senses on a particular object, and the gopīs indicate that the pastimes of Kṛṣṇa are the perfection of all meditation and samādhi. It is also confirmed in the Bhagavad-gītā that anyone who is always absorbed in the thought of Kṛṣṇa is the topmost of all yogīs.” (Kṛṣṇa book, Chapter 21)
All glories to Śrīla Prabhupāda!