On RJ-45/UTP with 2 pairs, (Tx, Rx) which pair will be used in case of half-duplex? How is decided and conveyed between the two ends, when auto-neg is not enabled?
For 10BASE-T and 100BASE-TX, the MDI side (NICs, routers) transmits on pairs 1-2 and receives on 3-6. On the MDI-X side (hubs, switches) the pairs are swapped. In general, concentrators use MDI-X pinout while edge devices (from the L2 segment perspective) use MDI pinout.
Whether the link uses full or half duplex doesn't matter.
Auto negotiation takes only care of speed and duplex settings. Automatic send/receive pair negotiation is called Auto MDI-X. Auto MDI-X is defined in IEEE 802.3 clause 40.4.4 and was added alongside 1000BASE-T in 802.3ab-1999.
Auto MDI-X can almost be taken for granted today. Devices not implementing it are rare, especially with gigabit+ ports where it doesn't even require any additional hardware.
Half-duplex mode in Ethernet still uses 2 pairs. The difference to full-duplex is that it only uses one pair at a time.
Half-duplex mode with twisted pair cables only exists because of hubs: Reason for half-duplex mode in Ethernet?
half-duplex mode support in Ethernet chipsets was crucial in case either a network hub (hub is internally a single wire) or some other shared Ethernet medium (for example, 10BASE-5) was used