Tactile contact is a key element of animal-assisted interventions (AAI), yet its effects on the animals involved remain poorly understood. Seven adult goats were included in the experiment, which examined three factors influencing tactile contact: the body region (head/neck, trunk, hindquarters; R1–R3), the ordinal position in the stroking sequence (first, second, third; O1–O3) and the location context (slightly enriched goat house and a highly enriched pasture; L1, L2). It was found that when stroking occurred first in the position of the sequence (O1), the duration of touch was significantly shorter (p < 0.0001). In addition, it was observed that when the session started with the trunk (R2), the total contact duration (T) was significantly longer (p < 0.039). No differences were found between the duration of contact in different locations (p = 0.179). These results may indicate that the initial phase was critical for the overall contact. Furthermore, the longer duration of contact, when initiated on the trunk, may indicate a relative preference for this body region. These findings suggest that human contact remains equally attractive to goats regardless of the enrichment of their location.