B.G 3.19

तस्मादसक्तः सततं कार्यं कर्म समाचर। असक्तो ह्याचरन् कर्म परमाप्नोति पूरुषः ॥१९॥

Therefore, practice the activities of duties without expectation of result. It is he who practices duties firmly without expectations that attains the highest good.

Gīta Tātparya 3.19

Perform duties with equanimity is the conclusion. Arjuna belongs to the category of beings eligible for liberation based on testimonials from Mahabharata. To say he belongs to the lower category is not appropriate (with reference to Advaita interpretation)

यस्मादमुक्तस्य कार्यमस्त्येव तस्मादसक्तः। असक्त आचरन्नेव यस्मात् परमाप्नोति। मुक्तस्यैव कार्यं नास्ति इत्येवकारार्थोऽपि यस्तु इति तुशब्देन अवगतः।

For one who is not liberated there are even activities. Therefore, he should become 'asakta', i.e. devoid of curiosity or expectation. By practicing only without expectation, one attains the Supreme. Only the liberated do not have activities is indicated by using the words 'ēva', i.e. 'only', and by the word 'yastu', i.e. 'he who' (3.17 'यस्त्वात्मरतिरेव'). "Therefore perform duties with equanimity" is the conclusion. Else, (if interpreted as no need to perfrom action), there is opposition.

"ब्रह्मनिष्ठा ब्रह्मरता ब्रह्मज्ञानसुतर्पिताः। पाण्डवानां च मुक्तानामन्तरं किञ्चिदेव हि॥"

"Being steadfast in the Brahman, delighting in the Brahman, and contented in the knowledge of the Brahman, indeed there is little difference between the Pandavas and the liberated."

इति भविष्यत्पर्ववचनाच्च न अर्जुनस्य अमुख्याधिकारिता। आत्मरतिरेव स्यादित्येव शब्देन मुक्तानामेभ्यो विशेषो दर्शितः। एषां कदाचिद् दुःखाभासस्यापि भावात् ॥१९॥

- thus is the statement from "Bhavishyad-Parva", indicating Arjuna does not belong to an ineligible category. The usage of words such as 'ātmaratirēva', i.e. 'one who delights in the lord', and 'syat', i.e. 'perhaps', specially shows they are addressed to those who are eligible for liberation. Even among them, sometimes misery is experienced.