We apply pre-trained architectures, originally developed for the ImageNet Large Scale Visual Recognition Challenge, for periocular recognition. These architectures have demonstrated significant success in various computer vision tasks beyond the ones for which they were designed. This work builds on our previous study using off-the-shelf Convolutional Neural Network (CNN) and extends it to include the more recently proposed Vision Transformers (ViT). Despite being trained for generic object classification, middle-layer features from CNNs and ViTs are a suitable way to recognize individuals based on periocular images. We also demonstrate that CNNs and ViTs are highly complementary since their combination results in boosted accuracy. In addition, we show that a small portion of these pre-trained models can achieve good accuracy, resulting in thinner models with fewer parameters, suitable for resource-limited environments such as mobiles. This efficiency improves if traditional handcrafted features are added as well.