There are many synonymous phrases that can be used instead of "giving sign to". Some examples include: signaling, indicating, gesturing, pointing out, hinting, showing, demonstrating, making a motion towards, and conveying. Each of these phrases suggests the act of conveying a message or information without explicitly stating it. Depending on the context, some phrases may be more appropriate than others. For example, signaling may be more appropriate in a military context, while hinting may be more appropriate in a social context. Ultimately, choosing the right phrase depends on the specific situation and desired tone.