Final answer:
The spider in question, found in Austin, Texas and displaying non-aggressive behavior, is likely one of the common harmless spiders rather than a venomous brown recluse. Accurate identification requires a clear photo or closer examination, but safety should be a priority by maintaining a safe distance.
Step-by-step explanation:
Based on the description and location provided, the spider you encountered likely falls under the category of common spiders found in Austin, Texas. While there are venomous species like the brown recluse in the region, most spiders you'll encounter are harmless and play a beneficial role by controlling insect populations. Unlike the brown recluse, many spiders do not have a distinctive violin-shaped mark on their backs. Moreover, their bodies and leg span can vary considerably. Considering its behavior and size, it is less likely to be a brown recluse, as they tend to be smaller and more reclusive.
To accurately identify the spider, a clear photograph or a closer examination would be necessary. However, without intending to handle or provoke it, it's advisable to maintain a safe distance to avoid any potential risk, especially if uncertain about the species. Spiders generally prefer to avoid humans and will typically flee rather than become aggressive. If you do suspect the spider is a brown recluse or another venomous species, it is best to consult with a local expert for proper identification and removal.