1	Ashvini	β and γ Arietis	Horse's head	27
1	wife of the Ashvins	Sheratan and Mesarthim	Horse's head	April 17 (107)
2	Bharani	35, 39, and 41 Arietis	Yoni, the female organ of reproduction	41 = 27 + 14
2	the bearer	Musca Borealis	Yoni, the female organ of reproduction	May 1 (121)
3	Krittikā	M 45 Tauri	Knife or spear	55 = 41 + 14
3	the nurses of Kārttikeya	The Pleiades	Knife or spear	May 15 (135)
4	Rohini	α Tauri	Cart or chariot, temple, banyan tree	68 = 55 + 13
4	the red one	Aldebaran	Cart or chariot, temple, banyan tree	May 28 (148)
5	Mrigashīrsha	λ, φ¹, and φ² Orionis	Deer's head	83 = 68 + 15
5	the deer's head	Heka	Deer's head	June 12 (163)

Also in the Arabic manzil system the 5th station is ruled by Heka, although July 9 (190) is a month later than June 12 (163), when the star rose heliacally:

Nawaa	Manzil	Begins on	Number of days		Stars
Al Thuraya	1. Sheratan	17 May (137)	14	14	Sheratan
	2. Pleione	31 May (151)	13	27	Pleione
	3. Albatain	13 June (164)	13	40	Albatain in the Pleiades
Al Tuwaibe'	4. Al Tuwaibe'	26 June (177)	13	53	Aldebaran
Al Jawzaa	5. Heka	9 July (190)	13	66	Heka
Al Jawzaa	6. Alhena	22 July (203)	13	79	Alhena

The name Sheratan (from Al Sharatain the dual form of Al Sharat, 'Sign') indicates both Sheratan (β) and Mesarthim (γ). May 17 (137) - April 17 (107) = 30.

Neither does Auriga appear in the Chinese list nor in the Tahitian star pillar list, only in Chaucer's list, where Hassaleh is named Al-kab ('the Heel'):

Chaucer's List
1	Alkab	ι Aurigae
2	Alpheta	α Coronae Borealis
3	Alramih	Arcturus
4	Alkaid	η Ursae Majoris
5	K. Alasad	α Leonis
6	Algomisa	α Canis Minoris
7	Alhabor	α Canis Majoris
8	Alghul	β Persei
9	Alnath	β Tauri
10	Markab	α Pegasi
11	Alradif	δ Cephei
12	Alnasir	α Andromedae

Possibly the reason for the non-appearance of Capella in the other lists is its location (46º N) which is outside the reach of the Moon.

"... the Moon can go overhead at latitudes up to 28° from the equator ..." (Wikipedia)

The Bharani star is at 27° 02' N, outside the reach of Sun.

In rongorongo times Capella rose in June 7 (158) = 51 days after Sheratan. Capella (78.4) - Sheratan (27.4) = 51.0. There are 14 days in the Sheratan manzil and 14 + 13 (Pleione) + 13 (Albatain) + 13 (Al Tuwaibe') = 53.