It would seem that, similarly to SN 48.36, bodily feeling based on the Suttas—in contrast to Abhidhamma, of which bodily feeling can only be pleasant or painful—could be neutral as well (along with pleasant and painful feeling). This is described in SN 36.7 (although not being completely conclusive, since, in a way, everything is 'dependent on this body').
SN 36.7 (transl., Bhikkhu Bodhi; Pāḷi, VRI edition) wrote:Bhikkhus, while a bhikkhu dwells thus, mindful and clearly comprehending, diligent, ardent, and resolute, if there arises in him a neither-painful-nor-pleasant feeling, he understands thus: ‘There has arisen in me a neither-painful-nor-pleasant feeling. Now that is dependent, not independent. Dependent on what? Dependent on just this body. But this body is impermanent, conditioned, dependently arisen. So when the neither-painful-nor-pleasant feeling has arisen in dependence on a body that is impermanent, conditioned, dependently arisen, how could it be permanent?’ He dwells contemplating impermanence in the body and in neither-painful-nor-pleasant feeling, he dwells contemplating vanishing, contemplating fading away, contemplating cessation, contemplating relinquishment. As he dwells thus, the underlying tendency to ignorance in regard to the body and in regard to neither-painful-nor-pleasant feeling is abandoned by him.
Tassa ce, bhikkhave, bhikkhuno evaṃ satassa sampajānassa appamattassa ātāpino pahitattassa viharato uppajjati adukkhamasukhā vedanā, so evaṃ pajānāti – ‘uppannā kho myāyaṃ adukkhamasukhā vedanā. Sā ca kho paṭicca, no appaṭicca. Kiṃ paṭicca? Imameva kāyaṃ paṭicca. Ayaṃ kho pana kāyo anicco saṅkhato paṭiccasamuppanno. Aniccaṃ kho pana saṅkhataṃ paṭiccasamuppannaṃ kāyaṃ paṭicca uppannā adukkhamasukhā vedanā kuto niccā bhavissatī’ti! So kāye ca adukkhamasukhāya ca vedanāya aniccānupassī viharati, vayānupassī viharati, virāgānupassī viharati, nirodhānupassī viharati, paṭinissaggānupassī viharati. Tassa kāye ca adukkhamasukhāya ca vedanāya aniccānupassino viharato…pe… paṭinissaggānupassino viharato, yo kāye ca adukkhamasukhāya ca vedanāya avijjānusayo, so pahīyati.
Regarding feelings based on sights, sounds, odours and tastes, I was still not certain if these were classed as a bodily feeling or mental feeling. Although, it could logically come under mental feeling.
In Bhikkhu Bodhi's translations of the MN/SN/AN, almost all of the many instances where 'bodily feeling' is mentioned, it is used with the stock expression:
[...] bodily feelings have arisen that are painful, racking, sharp, piercing, harrowing, disagreeable [...]”
It would clearly be false to consider feelings based of sights, sounds, odours and tastes largely capable of causing feelings that are 'racking, sharp, piercing...'.
There is also Bhikkhu Bodhi's note of which he mentions 'bodily sensitivity (kāyappasāda
)', the word seemingly based on the Abhidhamma, of which the compound doesn't seem to be in PED. Although, note the contradiction with bodily equanimity being equated to feelings based of sights, sounds, odours and tastes.
Note 212, SN 48.36, Bhikkhu Bodhi wrote:212 According to the Abhidhamma, all bodily feeling, that is, feeling arisen through bodily sensitivity (kāyappasāda), is either pleasant or painful; there is no neutral feeling based on bodily sensitivity. Hence Spk explains the bodily equanimity as feeling arisen based on the other four senses, the eye, etc.