There are some more points that imply the Shiva lingam is not a sexual organ.
1. If it is the union of sexual organs, then why does the name of Goddess Shakti not appear in the word Shiva lingam? It should have been called Shiva-Shakti lingam as is the case in Mallikarjuna Jyotirlinga where Mallika is the name of Goddess Parvati and Arjuna is the name of Lord Shiva.
Ardhanarishwara form of Lord Shiva is half Lord Shiva and half Goddess Parvati. In this word, “Nari” denotes the female aspect of Lord Shiva. Then why is there no name for the female aspect in Shiva lingam? Also, the temples where Shiva lingams are installed are called Lord Shiva temples and not Shiva-Parvati temples.
2. If the word Jyotirlinga means the sign of radiance and also other words like Prana Linga, Atma Linga, etc. are not related to sexuality, then why should Shiva lingam mean the phallus of Lord Shiva.
3. According to Jain and Buddhist scriptures, it is not related to sexuality.
4. Lord Shiva is considered an ascetic god. Therefore, it is less likely that there is any kind of sexuality associated with his symbol.
5. Assuming it is a phallus/mountain does not explain the shape of a Banalinga.
From the above arguments, we cannot definitely say that the Shiva lingam is related to sexuality, but it cannot be completely ruled out also. Most probably, sexuality was associated with it afterward.
Therefore, we can exclude mountain and phallus from our list.