I'm not answering about 13 because i'm unsure about it either being holy or unholy.(So, treat this as a partial answer)
However,I don't think that the number is 8(ashta) is inauspicious in Hinduism.
Because,we have many important(&auspicious) Hindu facts and facets related to it.
Few are given below:
The eight limbed path of Yoga viz:
Yama,Niyama,Asana,Pranayama,Pratyahara,Dharana,Dhyana & Samadhi.
The 8 manifestations of Maha Bhairava (a fierce form of Lord Shiva) viz
Kaala Bhairava, Asitaanga Bhairava, Rudra Bhairava, Krodha Bhairava,
Kapala Bhairava, Bhishana Bhairava, Unmatta Bhairava and Samhara
The 8 Rupas of Sri Maha Lakshmi viz:
Dhanya Lakshmi, Dhairya Lakshmi, Santana Lakshmi, Vijaya Lakshmi,
Vidya Lakshmi, Bhagya Lakshmi, Gaja Lakshmi, Vara Lakshmi
4)The Ashta Loka Palas:
The 8 guardians of directions viz:
The 8 principle queens of Lord Krishna viz:
Rukmini, Satyabhama, Jambavati, Nagnajiti, Mitravinda, Lakshmana,
Kalindi and Maadri.
6)The Ashta Matrikas:
Brahmani, Vaishnavi, Maheshwari, Aindri, Vaarahi, Chamunda, Naarasimhi
7)The Ashta Siddhis:
The 8 types of Super Natural powers obtained by Yoga sadhana viz:
8)The Ashta Vasus:
Who are among the 33 types of Vedic Deities viz:
Aapa, Dhruva, Soma, Dhara, Anila, Anala, Pratyusha and Prabhasa.
& 9)The Ashta Vinayakas or the 8 Ganeshas.
The only reason i can think of as to why number 8 might be regarded as inauspicious is because of its association with the frightening Sani Graha(Saturn) (According to "Numerology" Saturn is related to number 8).
Edit: regarding the importance of 13:
I could not any reference ,whatsoever, related to the significance of the number 13 in Hinduism .There are a horde of numbers that are significant in one or many ways but nothing could be found on 13.
The number 12 is significant ,for example,in many ways(The Dwadasa Rasis etc).Similarly the 14(the 14 Manvantaras) but i'm unable to find anything regarding 13.
Only reference of course being the case of Trayodashi Tithi which is ruled by Kamadeva .And the Pradosham Vrata (dedicated to Lord Shiva) is performed on those days.