search parameter passed to include
Your syntax is a bit off – the search() parameter doesn't accept multiple parameters, only a search query (e.g. .search('body:foobar')) or an object containing the search query plus search term options. In your case, you're actually passing an object (.search(entry.clientsOrAgency)), in which case Craft will look for a query parameter on that object (the second parameter is just ignored). Hence your error.

That being said, here's what you probably want:

{% set testimonial = craft.entries.section('testimonials').search('clientsOrAgency:'~type).order('RAND()').limit(1) %}


The above will search for entries in the testimonials section, which has the value equal to type in each clientsOrAgency field.

However – unless you need (which can be enabled as a default for all searching in Craft, or per-search using search term options mentioned above) for the clientsOrAgency field, I don't actually think using search() is the appropriate approach here. The following would be easier and probably more performant:

{% set testimonial = craft.entries.section('testimonials').clientsOrAgency(type).order('RAND()').limit(1) %}


Also, you should probably add .first() to your craft.entries query, in order to only pull a single entry:

{% set testimonial = craft.entries.section('testimonials').clientsOrAgency(type).order('RAND()').limit(1).first() %}

{% if testimonial %}
    ...
{% endif %}