You can create your own validator class by implementing EPiServer.Validation.IContentSaveValidate<T>. You cn find more info here https://world.episerver.com/documentation/developer-guides/CMS/Content/Validation/

Remove the required-attribute on DownloadPdfText, and add this class. Change CustomBlockType to your blocktype.

    public class CustomBlockValidator : IValidate<CustomBlockType>
    {
        IEnumerable<ValidationError> IValidate<CustomBlockType>.Validate(CustomBlockType customBlockType)
        {
            if (customBlockType.DisplayPdfButton && string.IsNullOrEmpty(customBlockType.DownloadPdfText))
            {
                return new[]
                        {
                            new ValidationError
                            {
                                ErrorMessage = "You can't hava a button without text, stupid!",
                                PropertyName = CustomBlockType.GetPropertyName(block => block.DownloadPdfText),
                                Severity = ValidationErrorSeverity.Error,
                                ValidationType = ValidationErrorType.AttributeMatched
                            }
                        };
            }
            

            return Enumerable.Empty<ValidationError>();
        }
    }